In Figure 1, the length of $¯ ¯¯¯¯¯¯¯¯ ¯ W Z$ is $3 a + 15$ and the length of $¯ ¯¯¯¯¯¯¯¯ ¯ W X$ is $7 a + 5$ . If $Y$ is the midpoint of $¯ ¯¯¯¯¯¯¯ ¯ X Z$ , calculate the length of $¯ ¯¯¯¯¯¯¯¯ ¯ W Y$ .

5 + 4 a

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5 - 2 a

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25 + 4 a

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20 + 5 a

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10 + 5 a

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Solution

The correct option is E $10 + 5 a$
Given that $W Z = 3 a + 15$ , $W X = 7 a + 5$
Therefore, we get $X Z = W Z - W X = 3 a + 15 - 7 a - 5 = 10 - 4 a$
Given that $Y$ is midpoint of $X Z$ , therefore we get
$\Rightarrow X Y = \frac{X Z}{2} = \frac{(10 - 4 a)}{2} = 5 - 2 a$
$\Rightarrow W Y = W X + X Y$
$= 7 a + 5 + 5 - 2 a$
$= 10 + 5 a$

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