Exercise 20 Page 54

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_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_1, we can use the x-coordinate of the midpoint, x_M= 5, and the given endpoint, x_2= 1.

x_M=x_1+x_2/2

SubstituteII

x_M= 5, x_2= 1

5=x_1+ 1/2

MultEqn

LHS * 2=RHS* 2

10=x_1+1

SubEqn

LHS-1=RHS-1

9=x_1

RearrangeEqn

Rearrange equation

x_1=9

The x-coordinate of the endpoint S is 9. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are -8 and 12, respectively.

y_M=y_1+y_2/2

SubstituteII

y_M= -8, y_2= 12

-8=y_1+ 12/2

MultEqn

LHS * 2=RHS* 2

-16=y_1+12

SubEqn

LHS-12=RHS-12

-28=y_1

RearrangeEqn

Rearrange equation

y_1=-28

The y-coordinate of S is -28, so point S is located at (9, -28).