what is the equation of the line, in slope- intercept form, that passes through (2, 4) and is...
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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
The distance, d, between the points (x1, y1) and (x2, y2) is
Derived from the Pythagorean Theorem
The Distance Formula
2122
12 yyxxd
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 (-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
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)
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
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
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