Determining the Length of Line Segment MN

What is the numerical length of line segment MN when point N lies on line segment MO with given values of MN, NO, and MO?

MN = 22

Explanation:

In this problem, we are given that point N lies on line segment MO, and we are provided with the values of MN, NO, and MO. We need to determine the length of line segment MN. Given: MN = 2x NO = x-2 MO = 2x+9 We know that for a point to lie on a line segment, the sum of two smaller segments is equal to the length of the larger segment. Therefore, we have: MO = NO + MN Substitute the given values into the equation: 2x + 9 = x - 2 + 2x Simplify by grouping like terms: 2x - x = -2 - 9 x = -11 Now, calculate the length of MN: MN = 2x MN = 2(11) MN = 22 Therefore, the length of line segment MN is 22 units.
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