Question

hd is the perpendicular bisector of ky such that point d lays on ky. dk = 7y + 17, hy = 4y + 33, dy = 10y - 22, and hk = 6y + 7. what is the length of ky?

Explanation:

Step1: Use property of perpendicular bisector

Since $HD$ is the perpendicular bisector of $KY$, we know that $DK = DY$. So, we set up the equation $7y + 17=10y - 22$.

Step2: Solve the equation for $y$

Subtract $7y$ from both sides: $17 = 3y-22$. Then add 22 to both sides: $3y=17 + 22=39$. Divide both sides by 3, we get $y = 13$.

Step3: Calculate the length of $KY$

Since $KY=DK + DY$ and $DK = DY$, we can also use $KY = 2DK$ (or $2DY$). Substitute $y = 13$ into the expression for $DK$: $DK=7y + 17=7\times13+17=91 + 17=108$. Then $KY = 2\times108 = 216$.

Answer:

216