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# The Midpoint Formula

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Graph the points A(-5, 0), B(3, 2), C(5, 6), and D(-3, 4).

Prove that ABCD is a parallelogram by showing that the

diagonals bisect each other (have the same midpoint).

Apr 21, 2021

#1
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The points are A(-5,0), B(3,2), C(5,6), D(-3,4) and diagonals are BD and AC.

Let midpoint of BD be (x,y).

$$x = {3-3 \over 2}$$

$$x = 0$$

$$y = {2+4 \over 2}$$

$$y = 3$$

∴ Midpoint of BC = (0,3)

Let midpoint of AD be (x',y')

$$x' = {-5+5 \over 2}$$

$$x' = 0$$

$$y' = {0+6 \over 2}$$

$$y' = 3$$

∴ Midpoint of AD = (0,3)

Thus, diagonals AC and BD bisect each other.

Hence ABCD is a ||gm.

Apr 21, 2021
#2
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Thank You so much!! amygdaleon305

Apr 21, 2021