Question

Y is the midpoint of XZ XY = 6X and YZ = 3x +3. Find XY, YZ, and XZ.

Answer 1

After setting the equal lengths of XY and YZ since Y is the midpoint, we solve for X, substitute back into the expressions for XY and YZ, and find that XY = YZ = 6, and XZ = 12.

Step-by-step explanation:

We are asked to find the lengths of segments XY, YZ, and XZ. Since Y is the midpoint of XZ, by definition, XY equals YZ. Given the equations XY = 6X and YZ = 3X + 3, we can set them equal to each other because they represent the same length. This gives us the equation 6X = 3X + 3. Solving for X yields:

• 6X - 3X = 3
• 3X = 3
• X = 1

Now substitute the value of X back into the original equations:

• XY = 6(1) = 6
• YZ = 3(1) + 3 = 6
• XZ = XY + YZ = 6 + 6 = 12

The lengths of segments XY, YZ, and XZ are 6, 6, and 12, respectively.