+136 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
+26393 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
\(\begin{array}{|rcll|} \hline XY &=& YZ \\ 3a +1 &=& a+9 \\ 2a &=& 8 \\ \mathbf{a} &=& \mathbf{4} \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline XZ &=& XY +YZ \\ XZ &=& (3a +1) + (a+9) \\ XZ &=& 4a+10 \quad | \quad a=4 \\ XZ &=& 4\cdot 4 + 10 \\ XZ &=& 16+10 \\ \mathbf{XZ} &=& \mathbf{26} \\ \hline \end{array}\)
