We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
93
2
avatar+106 

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
avatar+23281 
+3

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

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

 

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

 

laugh

 Sep 13, 2019
 #2
avatar+106 
+2

Thank you! 

Roxettna  Sep 13, 2019

28 Online Users

avatar