Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
3. Using Midpoint and Distance Formulas
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Exercise 21 Page 25

Let G be (x_2,y_2) and use the Midpoint Formula.

G(18,- 9)

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= 8, and the given endpoint, x_1= - 2.
x_M=x_1+x_2/2
8=- 2+x_2/2
16=- 2+x_2
18=x_2
x_2=18
The x-coordinate of the endpoint G is 18. Now, we will determine its y-coordinate in a similar process. The y-coordinates of the midpoint and given endpoint are 0 and 9, respectively.
y_M=y_1+y_2/2
0=9+y_2/2
0=9+y_2
- 9=y_2
y_2=- 9
The y-coordinate of G is - 9, so point G is located at (18,- 9).