Given:
[tex] XR=x+8 [/tex]
[tex] RY=4x-10 [/tex]
Since R is the midpoint of the line, we can set XR equal to RY and solve for x.
[tex] RY=XR [/tex]
[tex] 4x-10=x+8 [/tex]
[tex] 4x=x+18 [/tex]
[tex] 3x=18 [/tex]
[tex] x=6 [/tex]
Now we know what x is. We can plug in x to RY and XR and then add it all together to find XY. Let's find XR:
[tex] XR=6+8 [/tex]
[tex] XR=14 [/tex]
Let's find RY now:
[tex] RY=4(6)-10 [/tex]
[tex] RY=24-10 [/tex]
[tex] RY=14 [/tex]
Since we know that:
[tex] XR+RY=XY [/tex]
We can plug in our answers:
[tex] 14+14=XY [/tex]
Final answer:
[tex] XY=28 [/tex]
