Exercise 22 Page 401

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= - 132, and the given endpoint, x_1= - 4.

x_M=x_1+x_2/2

SubstituteII

x_M= -13/2, x_1= - 4

-13/2=- 4+x_2/2

MultEqn

LHS * 2=RHS* 2

- 13=- 4+x_2

AddEqn

LHS+4=RHS+4

- 9=x_2

RearrangeEqn

Rearrange equation

x_2=- 9

The x-coordinate of the endpoint H is - 9. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are - 6 and 1, respectively.

y_M=y_1+y_2/2

SubstituteII

y_M= - 6, y_1= 1

- 6=1+y_2/2

MultEqn

LHS * 2=RHS* 2

- 12=1+y_2

SubEqn

LHS-1=RHS-1

- 13=y_2

RearrangeEqn

Rearrange equation

y_2=- 13

The y-coordinate of H is - 13, so point H is located at (- 9,- 13).