Question

using the image below, solve for x and y.
17
26
2y + 1
3x - 10
x =
y =

Explanation:

Step1: Use the property of the perpendicular bisector

Since the line is a perpendicular bisector, the two segments \(3x - 10\) and \(26\) are equal.

$$3x-10 = 26$$

Step2: Solve the equation for \(x\)

Add \(10\) to both sides:

$$3x=26 + 10$$

$$3x=36$$

Divide both sides by \(3\):

$$x=\frac{36}{3}=12$$

Step3: Use the property of the perpendicular bisector for \(y\)

The two segments \(2y + 1\) and \(17\) are equal.

$$2y+1 = 17$$

Step4: Solve the equation for \(y\)

Subtract \(1\) from both sides:

$$2y=17 - 1$$

$$2y=16$$

Divide both sides by \(2\):

$$y=\frac{16}{2}=8$$

Answer:

\(x = 12\)
\(y = 8\)