11 x1 t05 01 division of an interval (2012)

Download 11 x1 t05 01 division of an interval (2012)

Post on 11-Jul-2015

531 views

Category:

Education

2 download

Embed Size (px)

TRANSCRIPT

<ul><li><p>Coordinate Geometry</p></li><li><p>Coordinate GeometryDistance Formula</p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y </p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p><p> 2 25 3 3 1d </p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p><p> 2 25 3 3 1d 2 22 4</p><p>20</p><p>2 5 units</p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p><p> 2 25 3 3 1d 2 22 4</p><p>20</p><p>2 5 units</p><p>The distance formula is finding the length of the hypotenuse, </p><p>using Pythagoras</p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p><p> 2 25 3 3 1d 2 22 4</p><p>20</p><p>2 5 units</p><p>Midpoint Formula</p><p>The distance formula is finding the length of the hypotenuse, </p><p>using Pythagoras</p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p><p> 2 25 3 3 1d 2 22 4</p><p>20</p><p>2 5 units</p><p>Midpoint Formula</p><p>1 2 1 2,2 2</p><p>x x y yM </p><p>The distance formula is finding the length of the hypotenuse, </p><p>using Pythagoras</p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p><p> 2 25 3 3 1d 2 22 4</p><p>20</p><p>2 5 units</p><p>Midpoint Formula</p><p>1 2 1 2,2 2</p><p>x x y yM e.g. Find the midpoint of </p><p>(3,4) and (2 ,1) </p><p>The distance formula is finding the length of the hypotenuse, </p><p>using Pythagoras</p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p><p> 2 25 3 3 1d 2 22 4</p><p>20</p><p>2 5 units</p><p>Midpoint Formula</p><p>1 2 1 2,2 2</p><p>x x y yM e.g. Find the midpoint of </p><p>(3,4) and (2 ,1) 3 2 4 1,</p><p>2 2M </p><p>The distance formula is finding the length of the hypotenuse, </p><p>using Pythagoras</p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p><p> 2 25 3 3 1d 2 22 4</p><p>20</p><p>2 5 units</p><p>Midpoint Formula</p><p>1 2 1 2,2 2</p><p>x x y yM e.g. Find the midpoint of </p><p>(3,4) and (2 ,1) 3 2 4 1,</p><p>2 2M </p><p>1 5,2 2</p><p>The distance formula is finding the length of the hypotenuse, </p><p>using Pythagoras</p></li><li><p>Coordinate GeometryDistance Formula</p><p> 2 22 1 2 1d x x y y e.g. Find the distance between </p><p>(1,3) and (3,5) </p><p> 2 25 3 3 1d 2 22 4</p><p>20</p><p>2 5 units</p><p>Midpoint Formula</p><p>1 2 1 2,2 2</p><p>x x y yM e.g. Find the midpoint of </p><p>(3,4) and (2 ,1) 3 2 4 1,</p><p>2 2M </p><p>1 5,2 2</p><p>The distance formula is finding the length of the hypotenuse, </p><p>using Pythagoras</p><p>The midpoint formula averages the x and y values</p></li><li><p>Division Of An Interval</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X Y</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X YA</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X YA</p><p>A divides XY internally in the ratio m:n</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X YA</p><p>A divides XY internally in the ratio m:n</p><p> m</p><p> n</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X YA</p><p>A divides XY internally in the ratio m:n</p><p> m</p><p> n</p><p> OR</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X YA</p><p>A divides XY internally in the ratio m:n</p><p> m</p><p> n</p><p> ORA divides YX internally in the ratio n:m</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X YA</p><p>X Y</p><p>A divides XY internally in the ratio m:n</p><p> m</p><p> n</p><p> ORA divides YX internally in the ratio n:m</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X YA</p><p>X Y A</p><p>A divides XY internally in the ratio m:n</p><p> m</p><p> n</p><p> ORA divides YX internally in the ratio n:m</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X YA</p><p>X Y A</p><p>A divides XY internally in the ratio m:n</p><p> m</p><p> n</p><p> ORA divides YX internally in the ratio n:m</p><p>A divides XY externally in the ratio m:n</p></li><li><p>Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1 </p><p>In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.</p><p>X YA</p><p>X Y A</p><p>A divides XY internally in the ratio m:n</p><p> m</p><p> n</p><p> ORA divides YX internally in the ratio n:m</p><p>A divides XY externally in the ratio m:n </p><p>m</p><p> n </p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points Set up your answer by drawing a set of parentheses with two </p><p>vinculums separated by a comma</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points Set up your answer by drawing a set of parentheses with two </p><p>vinculums separated by a comma</p><p> , P</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points Set up your answer by drawing a set of parentheses with two </p><p>vinculums separated by a comma</p><p> , P</p><p> Add the numbers in the ratio together to get the denominator</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points Set up your answer by drawing a set of parentheses with two </p><p>vinculums separated by a comma</p><p> , P</p><p> Add the numbers in the ratio together to get the denominator</p><p>4 4</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points Set up your answer by drawing a set of parentheses with two </p><p>vinculums separated by a comma</p><p> , P</p><p> Add the numbers in the ratio together to get the denominator</p><p>4 4</p><p> Multiply along the cross and add to get the numerator</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points Set up your answer by drawing a set of parentheses with two </p><p>vinculums separated by a comma</p><p> , P</p><p> Add the numbers in the ratio together to get the denominator</p><p>4 4</p><p> Multiply along the cross and add to get the numerator5133 </p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points Set up your answer by drawing a set of parentheses with two </p><p>vinculums separated by a comma</p><p> , P</p><p> Add the numbers in the ratio together to get the denominator</p><p>4 4</p><p> Multiply along the cross and add to get the numerator5133 6143 </p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points Set up your answer by drawing a set of parentheses with two </p><p>vinculums separated by a comma</p><p> , P</p><p> Add the numbers in the ratio together to get the denominator</p><p>4 4</p><p> Multiply along the cross and add to get the numerator5133 6143 </p><p> 4</p><p>18,44</p></li><li><p>Type 1: Internal Division</p><p>Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3</p><p> 4,32003 Extension 1 HSC Q1c)</p><p> 6,5 Write down the endpoints of the interval in the same order as </p><p>they are mentioned.</p><p> 4,3 6,5</p><p> Write down the ratio.</p><p>3:1</p><p> Draw a cross joining the ratio to the two points Set up your answer by drawing a set of parentheses with two </p><p>vinculums separated by a comma</p><p> , P</p><p> Add the numbers in the ratio together to get the denominator</p><p>4 4</p><p> Multiply along the cross and add to get the numerator5133 6143 </p><p> 4</p><p>18,44 </p><p>29,1</p></li><li><p>Type 2: External Division</p><p>Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.</p><p> 1,3 2004 Extension 1 HSC Q1c)</p><p> 2,9</p></li><li><p>Type 2: External Division</p><p>Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.</p><p> 1,3 2004 Extension 1 HSC Q1c)</p><p> 2,9 Done exactly the same as internal division, except make one of </p><p>the numbers in the ratio negative</p></li><li><p>Type 2: External Division</p><p>Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.</p><p> 1,3 2004 Extension 1 HSC Q1c)</p><p> 2,9 Done exactly the same as internal division, except make one of </p><p>the numbers in the ratio negative</p><p> 1,3 2,9</p></li><li><p>Type 2: External Division</p><p>Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.</p><p> 1,3 2004 Extension 1 HSC Q1c)</p><p> 2,9 Done exactly the same as internal divisi...</p></li></ul>