Pearson Geometry Common Core, 2011
PG
Pearson Geometry Common Core, 2011 View details
7. Midpoint and Distance in the Coordinate Plane
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Exercise 16 Page 54

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

(10, -20)

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= 0.
x_M=x_1+x_2/2
5=x_1+ 0/2
10=x_1+0
10=x_1
x_1=10
The x-coordinate of the endpoint S is 10. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are -8 and 4, respectively.
y_M=y_1+y_2/2
-8=y_1+ 4/2
-16=y_1+4
-20=y_1
y_1=-20
The y-coordinate of S is -20, so point S is located at (10, -20).