Question

ex7: find the values of x and y that make the segments shown below bisect each other.

Explanation:

Step1: Set up equations for bisection

When segments bisect each other, the lengths of the divided - parts are equal. So we set up two equations:
For the vertical segments: $y = 2x$.
For the horizontal segments: $5y=3x - 13$.

Step2: Substitute $y = 2x$ into the second equation

Substitute $y$ in the equation $5y=3x - 13$ with $2x$. We get $5(2x)=3x - 13$.
Expand the left - hand side: $10x=3x - 13$.

Step3: Solve for $x$

Subtract $3x$ from both sides of the equation $10x=3x - 13$:
$10x-3x=3x - 13-3x$.
$7x=-13$.
$x =-\frac{13}{7}$.

Step4: Solve for $y$

Substitute $x =-\frac{13}{7}$ into the equation $y = 2x$.
$y = 2\times(-\frac{13}{7})=-\frac{26}{7}$.

Answer:

$x =-\frac{13}{7},y =-\frac{26}{7}$