Exercise 37 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= -3, and the given endpoint, x_1= 0.

x_M=x_1+x_2/2

SubstituteII

x_M= -3, x_1= 0

-3=0+x_2/2

MultEqn

LHS * 2=RHS* 2

-6=0+x_2

IdPropAdd

Identity Property of Addition

-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 2 and 11, respectively.

y_M=y_1+y_2/2

SubstituteII

y_M= 2, y_1= 11

2=11+y_2/2

MultEqn

LHS * 2=RHS* 2

4=11+y_2

SubEqn

LHS-11=RHS-11

-7=y_2

RearrangeEqn

Rearrange equation

y_2=-7

The y-coordinate of K is -7, so point K is located at (-6,-7).