Exercise 35 Page 74

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= -1, and the given endpoint, x_1= -8.

x_M=x_1+x_2/2

SubstituteII

x_M= -1, x_1= -8

-1=-8+x_2/2

MultEqn

LHS * 2=RHS* 2

-2=-8+x_2

AddEqn

LHS+8=RHS+8

6=x_2

RearrangeEqn

Rearrange equation

x_2=6

The x-coordinate of the endpoint K is 6. Now, we can determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are 1 and 4, respectively.

y_M=y_1+y_2/2

SubstituteII

y_M= 1, y_1= 1

1=4+y_2/2

MultEqn

LHS * 2=RHS* 2

2=4+y_2

SubEqn

LHS-4=RHS-4

-2=y_2

RearrangeEqn

Rearrange equation

y_2=-2

The y-coordinate of K is -2, so point K is located at (6,-2).