Question

Point S is on line segment RT.Given RT = x + 5, ST = 4x – 9, and

RS = x - 2, determine the numerical length of RT.

RT =

Answer 1

9

Explanation:

Points R, S, and T are collinear.

RT = x + 5

ST = 4x - 9

RS = x - 2

First, create an equation to find the value of the variable x

RS + ST = RT (segment addition postulate)

(x - 2) + (4x - 9) = (x + 5) (substitution)

Solve for x

x - 2 + 4x - 9 = x + 5

Collect like terms

5x - 11 = x + 5

5x - x = 11 + 5

4x = 16

Divide both sides by 4

4x/4 = 16/4

x = 4

RT = x + 5

Plug in the value of x

RT = 4 + 5

RT = 9