Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
8. Coordinate Proofs
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Exercise 22 Page 644

Notice that all vertices are on either the y-axis or on the x-axis.

B

Practice makes perfect

Let's place the vertices in a coordinate plane. Two of the points, (w,0) and (- w,0) are both on the x-axis since their y-coordinates are 0. Also since w and - w are opposite numbers, they will be equally far away from the origin.

The remaining two points, (0,v) and (0,- v) are both on the y-axis since their x-coordinates are 0. Also because v and - v are opposite numbers, they are equally far away from the origin.

The midpoint we are looking for is on the side with (0,- v) and (- w,0) as endpoints. Using the Midpoint Formula, we can find this point.
M=(x_1+x_2/2,y_1+y_2/2)
M=(- w+ 0/2,0+( - v)/2)
â–Ľ
Simplify
M=(- w+0/2,0-v/2)
M=(- w/2,- v/2)
M=(- w/2,- v/2)
This corresponds to option B.