Exercise 21 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= 4.5.

x_M=x_1+x_2/2

SubstituteII

x_M= 5, x_2= 4.5

5=x_1+ 4.5/2

MultEqn

LHS * 2=RHS* 2

10=x_1+4.5

SubEqn

LHS-4.5=RHS-4.5

5.5=x_1

RearrangeEqn

Rearrange equation

x_1=5.5

The x-coordinate of the endpoint S is 5.5. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are -8 and -2.5, respectively.

y_M=y_1+y_2/2

SubstituteII

y_M= -8, y_2= -2.5

-8=y_1+( -2.5)/2

AddNeg

a+(- b)=a-b

-8=y_1-2.5/2

MultEqn

LHS * 2=RHS* 2

-16=y_1-2.5

AddEqn

LHS+2.5=RHS+2.5

-13.5=y_1

RearrangeEqn

Rearrange equation

y_1=-13.5

The y-coordinate of S is -13.5, so point S is located at (5.5, -13.5).