Question

Identify the segment

Answer 1

line l

MQ = 7

Explanation:

A segment bisector is a geometric object, such as a line, ray, or another line segment, that divides a given line segment into two equal parts. In the case of line segment PQ, its segment bisector is represented by line l.

Since line l bisects the line segment PQ at point M, it follows that PM is equal to MQ. To determine the length of MQ, we first need to find the value of x. To do this, we'll set the expressions for PM and MQ equal to each other and solve for x:

`\begin{aligned}PM&=MQ\\5x-3&=11-2x\\5x-3+2x&=11-2x+2x\\7x-3&=11\\7x-3+3&=11+3\\7x&=14\\7x/ 7&=14 / 7\\x&=2\end{aligned}`

Now that we have found the value of x, we can substitute it into the expression for MQ:

`\begin{aligned}MQ&=11-2(2)\\MQ&=11-4\\MQ&=7\end{aligned}`

Therefore, the length of MQ is 7 units.