Exercise 19 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= -2.

x_M=x_1+x_2/2

SubstituteII

x_M= 5, x_2= -2

5=x_1+( -2)/2

AddNeg

a+(- b)=a-b

5=x_1-2/2

MultEqn

LHS * 2=RHS* 2

10=x_1-2

AddEqn

LHS+2=RHS+2

12=x_1

RearrangeEqn

Rearrange equation

x_1=12

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

y_M=y_1+y_2/2

SubstituteII

y_M= -8, y_2= 8

-8=y_1+ 8/2

MultEqn

LHS * 2=RHS* 2

-16=y_1+8

SubEqn

LHS-18=RHS-18

-24=y_1

RearrangeEqn

Rearrange equation

y_1=-24

The y-coordinate of S is -24, so point S is located at (12, -24).