The required value of z is 5.
Given that,
In RST, X is the midpoint of RS,
And Y is the midpoint of RT.
XY = 3z + 2 and ST = 7z - 1.
We have to determine,
What is the value of z.
According to the question,
X is the midpoint of RS,
And Y is the midpoint of RT.
Therefore,
[tex]XY = \frac{ST}{2}[/tex]
Putting the value of XY and ST in the equation,
XY = 3z + 2 and ST = 7z - 1.
Then,
[tex]XY = \frac{RS}{2} \\\\3z+ 2 = \frac{7z-1}{2}\\\\2 \times(3z+2) = 7z-1\\\\= 6z+4= 7z-1\\\\6z-7z = -1-4\\\\-z = -5\\\\= z = 5[/tex]
Hence, The required value of z is 5.
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