For 99 pts and Brainliest The vertices of kite DEFG are (5, 5), (8, 2), (5, -4), and (2, 2), respectively. Prove that the diagon

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For 99 pts and Brainliest The vertices of kite DEFG are (5, 5), (8, 2), (5, -4), and (2, 2), respectively. Prove that the diagon

als of kite DEFG are perpendicular lines.

Mathematics

1 answer:

Brums [2.3K] · Answer 1 · 2022-08-11T21:36:45+03:00

Answer:

See below

Step-by-step explanation:

<em>Vector argument</em>

Vector DF is (5, -4) - (5, 5) = (0, -9).

Vector EG is (2, 2) - (8, 2) = (-6, 0).

The dot-product of these two vector is (0, -9)•(-6, 0) = 0·(-6) + (-9)·0 = 0.

When the dot-product of two vectors is zero, those vectors are at right-angles to each other. Therefore diagaonal DF ⊥ diagonal EG.

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<em>Alternate argument</em>

The x-coordinates of points D and F are the same, so diagonal DF is a vertical line. The y-coordinates of points E and G are the same, so diagonal EG is a horizontal line. Vertical lines are perpendicular to horizontal lines, so DF ⊥ EG.