GeometryUnit8:CoordinateGeometry
Ms.Talhami 1
GeometryUnit8:CoordinateGeometry
Name_________________
GeometryUnit8:CoordinateGeometry
Ms.Talhami 2
HelpfulVocabularyWord Definition/Explanation Examples/HelpfulTips
GeometryUnit8:CoordinateGeometry
Ms.Talhami 3
In the given triangles below, find the values for x. Find the distance between the two endpoints of each line segment:
12
16
x x
8
15
GeometryUnit8:CoordinateGeometry
Ms.Talhami 4
Now find the distance between the two endpoints of the line segment below:
DistanceFormula
GeometryUnit8:CoordinateGeometry
Ms.Talhami 5
Practice Find the distance between the two endpoints of each line segment:
Find the distance between each set of points:
(-3, 2) and (-9, -6)
(2, -3) and (6, 0) (1, 2) and (-11, 7)
(2, 2) and (6, 5)
(-3, 0) and (3, 8) (0, 1) and (-4, -2)
(-2, 1) and (-5, 5)
(0, 0) and (-5, 12) (0, 1) and (3, 5)
Take it a Step Further
Show that the triangle with the following vertices is isosceles: 1,0 , 5,0 , %&'(3,4)
GeometryUnit8:CoordinateGeometry
Ms.Talhami 6
Midpoint
Identify the number that is exactly in the middle of each pair of numbers:
2 10
-16 -4
-7 7 Find the midpoint of the following line segments:
GeometryUnit8:CoordinateGeometry
Ms.Talhami 7
Now find the midpoint of the following line segment:
MidpointFormula
GeometryUnit8:CoordinateGeometry
Ms.Talhami 8
Practice Find the midpoint of the following line segments:
Find the midpoint for each set of points:
(-3, 2) and (-9, -6)
(2, -2) and (6, 0) (1, 2) and (-11, 8)
(2, 1) and (6, 5)
(-3, 0) and (3, 8) (0, 1) and (-4, -3)
(-2, 1) and (-6, 5)
(0, 0) and (-4, 12) (-1, 1) and (3, 5)
GeometryUnit8:CoordinateGeometry
Ms.Talhami 9
Slope In your own words, write down a definition for slope. Identify the types of slopes:
Practice Finding Slope 1) (8, 10), (−7, 14) 2) (−3, 1), (−17, 2) 3) (−20, −10), (−12, −4) 4) (−12, −5), (0, −8) 5) (−19, −6), (15, 16) 6) (−6, 9), (7, −9) 7) (−18, −20), (−18, −15) 8) (11, −18), (12, 12) 9) A line segment has endpoints (1, 5) and (3, k), and a slope of 4. Find the value of k, and the midpoint of the line segment.
GeometryUnit8:CoordinateGeometry
Ms.Talhami 10
Parallel and Perpendicular Slopes Parallel Slopes Perpendicular Slopes
Determine if the points passing through line L1 and line L2 are parallel, perpendicular, or neither.
f. Is it possible for two lines with negative slopes to be perpendicular? Explain why or why not.
GeometryUnit8:CoordinateGeometry
Ms.Talhami 11
Equations of Lines
Do Now: Find the slope of a line that passes through the points (-3, -4) and (5, 4). What do we know about the equation of a line?
Write the equation of the lines below:
GeometryUnit8:CoordinateGeometry
Ms.Talhami 12
Find the equation for each line with the given information: a. Passes through: (1, 0) Slope: 2
b. Passes through: (2, 1) Slope: 3/4
c. Passes through: (-3, 4) Slope: -1/2
d. Passes through: (-4, -1) Y-intercept: 5
e. Passes through: (8, 6) Y-intercept: -2
f. Passes through: (-6, 4) Y-intercept: 0
g. Passes through: (3, 3)and (-3, 7)
h. Passes through: (8, 5) and (1, 3) i. Passes through: (4, a) and (-5, a)
1) Find the equation of the line that passes through the point (5, -4) and has a slope of -2. 2) Find the equation of the line that passes through the point (4, 3) and has a y-intercept of -3. 3) Find the equation of the line that passes through the points (-2, 5) and (6, -1). 4) If the point (5,k) lies on the line represented by the equation - = −21 + 9, what is the value of k?
GeometryUnit8:CoordinateGeometry
Ms.Talhami 13
Write the equations for the line segments of the function on the graph below for the given domains: (a) -7<x<-4(b) -4<x<0 (c) 0<x<2(d) 2<x<6 (e) 6<x<7
Parallel and Perpendicular Lines
1) Write the equation of the line -1 that passes through the points (-4, 5) and (2, -4). 2) Write a second equation for the line -2 that passes through the points (-5, 0) and (4, 6). 3) Write a third equation for the line -3 that passes through the points (-3, -1) and (1, -7). 4) Graph and label all three equations on the set of axes: What do you notice about the slopes of equations -1 and -2? What do you notice about the slopes of equations -1 and -3?
GeometryUnit8:CoordinateGeometry
Ms.Talhami 14
Practice
1) Find the slope of a line parallel to a line with the given slopes:
23 -3 5 −12
2) Find the slope of a line perpendicular to a line with the given slopes:
23 -3 5 −12
3) Identify whether the following equations are parallel, perpendicular, or neither:
- = 21 + 6- = 41– 1
31 + 4- = 961 + 8- = 4
21– 5- = 10101– 4- = 16
41– 2- = 661 + 3- = 8
4) Write the equation of a line parallel to - = 7
8 1– 1 that passes through the point (-2, 3). 5) Write the equation of a line perpendicular to - = − 8
9 1– 3 that passes through the point (3, 4).
GeometryUnit8:CoordinateGeometry
Ms.Talhami 15
6) A line perpendicular to - = 78 1 + 3 passes through the point (1, -4). At which point do these two lines
intersect? Draw both lines on the graph below and label their point of intersection:
GeometryUnit8:CoordinateGeometry
Ms.Talhami 16
Perpendicular Bisectors
Find the midpoint of the line segment with endpoints (-5, -4) and (7, 6). Find the equation for this line segment on the given interval. Create an equation for a new line that also passes through this midpoint. Graph the line segment, midpoint, and your new line on the set of axes. What do we know about perpendicular bisectors?
How can we find the perpendicular bisector for the line segment with endpoints (-1, 4) and (3, -2)?
GeometryUnit8:CoordinateGeometry
Ms.Talhami 17
Practice 1) Find the equation of the perpendicular bisector of the line segment joining the points (-3, 5) and (3, -1). 2) The line - = − :
; 1 + 2 is the perpendicular bisector of a line segment that has an endpoint of (5, 6). Find the other endpoint. 3) Given two line segments, one joining points (-5, 0) and (1, 6) and the other joining points (2, 4) and (6, -2), find the coordinate where their perpendicular bisectors intersect. Then, draw the segments and their perpendicular bisectors on the graph below: