Huzefa K. answered • 04/19/14

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Math Teacher|Michigan + Northwestern Law|Perfect Score Math ACT + SAT

Hi L-

I will roll through the questions in the order posted:

1. The distance can be found using the distance formula (which is derived from the Pythagorean theorem):

___________________

\/ (x

_{1}- x_{2})^{2}+ (y_{1}- y_{2})^{2} ___________________

\/ (-2 - 5)

\/ (-2 - 5)

^{2}+ (3 - 4)^{2} ______ _

\/ 49 + 1 = 5\/2

\/ 49 + 1 = 5\/2

2. This just involves taking the mean of the x and y coordinates. So, you get

(-2 + 5)/2 = 1.5

(3 + 4)/2 = 3.5

C = (1.5, 3.5)

3. First, use point slope formula for the equation of the line with those two points:

y - y

_{1}= m(x - x_{1})m = (y

_{1}- y_{2})/(x_{1}- x_{2})m = (6 - 2)/(6 - 2) = 1

y - 2 = 1(x - 2)

y = x

Now all we do is find the midpoint of the line to know where the perpendicular bisector hits. As we saw above, we can calculate the midpoint to be (4, 4). Now, this line, since its perpendicular, will have a negative inverse slope of the original line. Therefore, it will be -1. So, the equation for the line is:

y - 4 = -1(x - 4)

y = -x + 4 + 4

y = -x + 8

4. The equation for a circle is as follows:

(x-a)

^{2}+ (y-b)^{2}= r^{2}where a and b are the coordinates of the center, and r is the radius.So, you get:

(x-0)

^{2}+ (y-0)^{2}= 6^{2}x

^{2}+ y^{2}= 365. Using the equation above:

(x+2)

^{2}+ (y+3)^{2}= 64Let me know if you have any questions.