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.