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# in the diagram, point y is the midpoint of seg. XZ, XY=3a +1, & YZ=a+9 for some constant, a. find the length of segment XZ

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in the diagram, point Y is the midpoint of seg. XZ, XY = 3a +1, & YZ = a+9 for some constant, a. find the length of segment XZ. Pls help

I tried to solve it as the following: XZ=XY^2 + YZ^2

XZ= (3a+1)^2 = a^2 + 9^2

a^2+16a+1+81

16a-1+81-1 = 81/1 = 81

or

XZ= (3a+1)^2 = a^2 + 9^2

a^2+16a+16+81

16a-16+81-16 = 65/16 = 4.06

Sep 13, 2019

#1
+23133
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In the diagram, point Y is the midpoint of seg. XZ, XY = 3a +1, & YZ = a+9 for some constant, a. find the length of segment XZ.

If Y is the midpoint of XZ, then XY=YZ

$$\begin{array}{|rcll|} \hline XY &=& YZ \\ 3a +1 &=& a+9 \\ 2a &=& 8 \\ \mathbf{a} &=& \mathbf{4} \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline XZ &=& XY +YZ \\ XZ &=& (3a +1) + (a+9) \\ XZ &=& 4a+10 \quad | \quad a=4 \\ XZ &=& 4\cdot 4 + 10 \\ XZ &=& 16+10 \\ \mathbf{XZ} &=& \mathbf{26} \\ \hline \end{array}$$

Sep 13, 2019
#2
+100
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Thank you!

Roxettna  Sep 13, 2019