Question

1.) the endpoints of $overline{cd}$ are given. find the coordinates of the midpoint m. (see example 1)
a. c(3, -5) and d(7, 9)
b. c(-8, -6) and d(-4, 10)
2.) the midpoint m and one endpoint of $overline{gh}$ are given. find the coordinates of the other endpoint. (see example 2.)
a. g(5, -6) and m(4, 3)
b. h(-2, 9) and m(8, 0)
3.) find the distance between the two points. (see example 3.)
a. a(9, 2) and b(7, 10)
b. c(-6, 5) and d(-3, 1)
c. e(3, 7) and f(6, 5)
d. l(7, -1) and m(-2, 4)

Explanation:

for 1a:

Step1: Calculate x-coordinate

$\frac{3+7}{2}=5$

Step2: Calculate y-coordinate

$\frac{-5+9}{2}=2$

for 1b:

Step1: Calculate x-coordinate

$\frac{-8+(-4)}{2}=-6$

Step2: Calculate y-coordinate

$\frac{-6+10}{2}=2$

for 2a:

Step1: Calculate x-coordinate of H

$2\times4 -5=3$

Step2: Calculate y-coordinate of H

$2\times3 -(-6)=12$

for 2b:

Step1: Calculate x-coordinate of G

$2\times8 -(-2)=18$

Step2: Calculate y-coordinate of G

$2\times0 -9=-9$

Answer:

1a. (5, 2)
1b. (-6, 2)
2a. (3, 12)
2b. (18, -9)
3a. $2\sqrt{17}$
3b. 5
3c. $\sqrt{13}$
3d. $\sqrt{106}$