Big Ideas Math Geometry, 2014
BI
Big Ideas Math Geometry, 2014 View details
Chapter Review
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Exercise 12 Page 57

Let K be (x_2,y_2), then use the Midpoint Formula.

K(-2,-3)

Practice makes perfect
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= 6, and the given endpoint, x_1= 14.
x_M=x_1+x_2/2
6=14+x_2/2
12=14+x_2
-2=x_2
x_2=-2
The x-coordinate of the endpoint K is -2. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are 3 and 9, respectively.
y_M=y_1+y_2/2
3=9+y_2/2
6=9+y_2
-3=y_2
y_2=-3
The y-coordinate of K is -3, so point K is located at (-2,-3).