Chapter 4.4, Problem 18PPS

To determine

To find: Whether the diagonals of a kite are perpendicular or not.

Answer to Problem 18PPS

Yes, the diagonals of a kite are perpendicular.

Explanation of Solution

Given information: The given kiteCDEF is shown where $C\left(0,0\right),D\left(8,1\right),E\left(9,6\right)\text{ and }F\left(4,7\right)$

Calculation: For diagonals of kite CDEF to be perpendicular, the slopes of CE and DF must be negative reciprocal to each other. Therefore, calculating slope $\left(m_{CE}\right)$ of CE and $\left(m_{DF}\right)$ of DF,

  $\begin{array}{c}{m}_{CE}=\frac{6-0}{9-0}\\ =\frac{2}{3}\mathrm{......}\left(1\right)\\ m_{DF}=\frac{7-1}{4-8}\\ =-\frac{3}{2}\mathrm{......}\left(2\right)\end{array}$

Now from (1) and (2), the slopes $\left(m_{CE}\right)$ of CE and $\left(m_{DF}\right)$ of DF are negative reciprocal to each other. Therefore, the diagonals are perpendicular.