Exercise 2 Page 53

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= 5, and the given endpoint, x_1= 3.

x_M=x_1+x_2/2

SubstituteII

x_M= 5, x_1= 3

5=3+x_2/2

MultEqn

LHS * 2=RHS* 2

10=3+x_2

SubEqn

LHS-3=RHS-3

7=x_2

RearrangeEqn

Rearrange equation

x_2=7

The x-coordinate of the endpoint C is 3. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are -2 and 4, respectively.

y_M=y_1+y_2/2

SubstituteII

y_M= -2, y_1= 4

-2=4+y_2/2

MultEqn

LHS * 2=RHS* 2

-4=4+y_2

SubEqn

LHS-4=RHS-4

-8=y_2

RearrangeEqn

Rearrange equation

y_2=-8

The y-coordinate of C is -8, so point C is located at (7,-8).