Exercise 7 Page 398

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= 2, and the given endpoint, x_1= 1.

x_M=x_1+x_2/2

SubstituteII

x_M= 2, x_1= 1

2=1+x_2/2

MultEqn

LHS * 2=RHS* 2

4=1+x_2

SubEqn

LHS-1=RHS-1

3=x_2

RearrangeEqn

Rearrange equation

x_2=3

The x-coordinate of the endpoint U is 3. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are 4 and 1, respectively.

y_M=y_1+y_2/2

SubstituteII

y_M= 4, y_1= 1

4=1+y_2/2

MultEqn

LHS * 2=RHS* 2

8=1+y_2

SubEqn

LHS-1=RHS-1

7=y_2

RearrangeEqn

Rearrange equation

y_2=7

The y-coordinate of U is 7, so point U is located at (3,7).