Question

On a coordinate plane, kite U V W X with diagonals is shown. Point U is at (negative 2, 5), point V is at (5, 4), point W is at (8, negative 5), and point X is at (negative 1, negative 2).
Prove that the diagonals of kite UVWX are perpendicular.



Step 1: Determine the slope of XV.



The slope of XV is
.





Step 2: Determine the slope of UW.



The slope of UW is
.



Step 3: The slopes of the diagonals are
.



The diagonals of kite UVWX are

Answer 1

Step 1: Slope of XV between X(-1, -2) and V(5, 4):
slope = (4 - (-2)) / (5 - (-1)) = 6 / 6 = 1.

Step 2: Slope of UW between U(-2, 5) and W(8, -5):
slope = (-5 - 5) / (8 - (-2)) = -10 / 10 = -1.

Step 3: The slopes of the diagonals are 1 and -1. Since 1 · (−1) = −1, the slopes are negative reciprocals, so the diagonals are perpendicular.