Question

use the figure below to answer questions #19 - 20. find the value of xy. y is the mid - point of $overline{xz}$. #19: xy = 6x - 3 and yz = 5x + 6 your answer #20: xy = 4x + 7 and yz = 8x - 1 your answer

Explanation:

Step1: Use mid - point property

Since Y is the mid - point of XZ, then $XY = YZ$. For question #19, we set up the equation $6x−3 = 5x + 6$.
$6x−3=5x + 6$

Step2: Solve for x

Subtract $5x$ from both sides: $6x-5x-3=5x - 5x+6$, which simplifies to $x-3 = 6$. Then add 3 to both sides: $x=6 + 3$, so $x = 9$.

Step3: Find the value of XY

Substitute $x = 9$ into the expression for XY. $XY=6x−3=6\times9−3=54 - 3=51$.

For question #20:

Step1: Use mid - point property

Set up the equation $4x + 7=8x−1$ since $XY = YZ$.
$4x + 7=8x−1$

Step2: Solve for x

Subtract $4x$ from both sides: $4x-4x + 7=8x-4x−1$, which gives $7 = 4x−1$. Add 1 to both sides: $7 + 1=4x-1 + 1$, so $8 = 4x$. Divide both sides by 4: $x = 2$.

Step3: Find the value of XY

Substitute $x = 2$ into the expression for XY. $XY=4x + 7=4\times2+7=8 + 7=15$.

Answer:

#19: 51
#20: 15