What is the equation of the line, in slope-intercept form, that passes through (2, 4) and is perpendicular to 5x+7y-1=0

Warm-Up: October 31, 2011

Homework Questions?

Distance and Midpoint Formulas;

CirclesSection 1.3

The distance, d, between the points (x1, y1) and (x2, y2) is

Derived from the Pythagorean Theorem

The Distance Formula

2122

12 yyxxd

Find the distance between (3, 7) and (-2, 4)

Example 1 (like HW #1-18)

Find the distance between (-5, 6) and (1, -1)

You-Try #1 (like HW #1-18)

The midpoint of a line segment with the endpoints (x1, y1) and (x2, y2) is

Average the x’s and average the y’s

The Midpoint Formula

2,

22121 yyxx

Find the midpoint of the line segment with endpoints (-3, 5) and (7, -9)

Example 2 (like HW #19-30)

Find the midpoint of the line segment with endpoints (-1, -2) and (3, 4)

You-Try #2 (like HW #19-30)

A circle is the set of all points in a plane that are equidistant from a fixed point, called the center.

The center is at (h, k) The fixed distance from the circle’s center

to any point on the circle is called the radius.

The radius is r.

Circle

Center at (h,k) Radius = r

The Standard Form of the Equation of a Circle

222 rkyhx

Write the standard form of the equation of the circle with center (3, -4) and radius 5.

Example 4 (like HW #31-40)

Write the standard form of the equation of the circle with center (-2, 1) and radius 6.

You-Try #4 (like HW #31-40)

Page 148 #1-37 every other odd

Assignment

The endpoints of a line segment are located at (4, -5) and (-2, -7).

a) Find the length of the line segment (distance between the endpoints).

b) Find the midpoint of the line segment.

Warm-Up: November 1, 2011

Homework Questions?

1. Find the center.2. Graph the center.3. Find the radius, r.4. Count out from the center r units in each

direction (up, down, right, left) and plot a point.

5. Draw a circle around those 4 points (try to make it look more like a circle than Mr. Szwast’s circles)

Graphing a Circle

Give the center and radius of the circle described by the equation below and graph it

Example 5 (like HW #41-48)

932 22 yx

Give the center and radius of the circle described by the equation below and graph it

You-Try #5 (like HW #41-48)

1613 22 yx

The General Form of the Equation of a Circle

022 FEyDxyx

Completing the Square Given x2 + Dx, we can create a perfect

square trinomial by dividing D by 2, squaring it, and adding it

Can complete the square for x’s and y’s separately

Remember that whatever you add to one side, you must add to the other side

222

22

Dx

DDxx

Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the equation.

Example 6 (like HW #49-56)

0461222 yxyx

Complete the square and write the equation in standard form. Then give the center and radius of the circle and graph the equation.

You-Try #6 (like HW #49-56)

0912422 yxyx

Page 148 #1-37 Every Other Odd Page 149 #41-57 Every Other Odd

Assignment