Question

1. $overline{hd}$ is the perpendicular bisector of $overline{ky}$. point $d$ lays on $overline{ky}$. $dk = 7y + 17$, $hy=4y + 33$, $dy = 10y - 22$, and $hk = 6y + 7$. a. find the value of $y$. b. what is the length of $dk$?

Explanation:

Step1: Set up equation

Since $HD$ is perpendicular bisector of $KY$, $HY = DY$. So $7y + 17=4y + 33$.

Step2: Solve for $y$

$7y-4y=33 - 17$, $3y = 16$, $y = 5$.

Step3: Find $DK$

Substitute $y = 5$ into $DK=10y - 22+6y + 7$, $DK=10\times5-22 + 6\times5+7=52$.

Answer:

a. $y = 5$
b. $DK = 52$