Pearson Geometry Common Core, 2011
PG
Pearson Geometry Common Core, 2011 View details
5. Conditions for Rhombuses, Rectangles, and Squares
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Exercise 35 Page 388

Let the coordinates of Q be (x_2,y_2). Use the Midpoint Formula.

Coordinates: Q(5, - 2)
Explanation: See solution.

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_2/2To find x_2, we can use the x-coordinate of the midpoint, which is x_M= - 1, and the x-coordinate of the given endpoint, which is x_1= - 7.
x_M=x_1+x_2/2
- 1=- 7+x_2/2
- 2=- 7 + x_2
5 = x_2
x_2 = 5
The x-coordinate of the endpoint Q is 5. Now, we will determine its y-coordinate by following a similar process. The y-coordinates of the midpoint and given endpoint are 4 and 10, respectively.
y_M=y_1+y_2/2
4=10+y_2/2
8 = 10 + y_2
- 2 = y_2
y_2 = - 2
The y-coordinate of Q is - 2, so point Q is located at (5, - 2).