Exercise 20 Page 25

We can use the Midpoint Formula to find the missing endpoint by splitting the usual formula into two separate equations, one for the x-coordinate and one for the y-coordinate. M(x,y)=(x_1+x_2/2, y_1+y_2/2) ⇕ x_M=x_1+x_2/2 and y_M=y_1+y_2/2 To find x_2, we can use the x-coordinate of the midpoint, x_M= - 2, and the given endpoint, x_1= - 3.

x_M=x_1+x_2/2

SubstituteII

x_M= - 2, x_1= - 3

- 2=- 3+x_2/2

MultEqn

LHS * 2=RHS* 2

- 4=- 3+x_2

AddEqn

LHS+3=RHS+3

- 1=x_2

RearrangeEqn

Rearrange equation

x_2=- 1

The x-coordinate of the endpoint G is - 1. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are 5 and 7, respectively.

y_M=y_1+y_2/2

SubstituteII

y_M= 5, y_1= 7

5=7+y_2/2

MultEqn

LHS * 2=RHS* 2

10=7+y_2

SubEqn

LHS-7=RHS-7

3=y_2

RearrangeEqn

Rearrange equation

y_2=3

The y-coordinate of G is 3, so point G is located at (- 1,3).