Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
7. Midpoint and Distance in the Coordinate Plane
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Exercise 17 Page 54

Let S be (x_1,y_1) and use the Midpoint Formula.

(5,-1)

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_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_1, we can use the x-coordinate of the midpoint, x_M= 5, and the given endpoint, x_2= 5.
x_M=x_1+x_2/2
5=x_1+ 5/2
10=x_1+5
5=x_1
x_1=5
The x-coordinate of the endpoint S is 5. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are -8 and -15, respectively.
y_M=y_1+y_2/2
-8=y_1+( -15)/2
-8=y_1-15/2
-16=y_1-15
-1=y_1
y_1=-1
The y-coordinate of S is -1, so point S is located at (5, -1).