Question

hd is the perpendicular bisector of ky such that point d lays on ky. ky = 7y - 14, hy = 4y + 33, and hk = 6y + 7. when the perpendicular bisector theorem is applied, what is the value of y? y = units

Explanation:

Step1: Apply perpendicular - bisector theorem

Since $HD$ is the perpendicular bisector of $KY$, by the perpendicular - bisector theorem, $HK = HY$.
So, we set up the equation $6y + 7=4y + 33$.

Step2: Solve the equation for $y$

Subtract $4y$ from both sides: $6y-4y + 7=4y-4y + 33$, which simplifies to $2y+7 = 33$.
Then subtract 7 from both sides: $2y+7 - 7=33 - 7$, getting $2y=26$.
Divide both sides by 2: $\frac{2y}{2}=\frac{26}{2}$, so $y = 13$.

Answer:

$13$