Question

: Which expression represents the measure of segment RS?

A) 3x−4
B) 4x+1
C) T−S
D) R÷(3x−S)

Answer 1

The expression that represents the measure of segment RS is
`\(3x - 4\)`

The correct answer is Option A.

Step-by-step explanation:

The measure of segment RS is often denoted by the difference between the coordinates of its endpoints. In this case, if R and S have coordinates represented by x and T respectively, then the measure of segment RS would be
`\(T - x\).` Now, looking at the given options,
`\(3x - 4\)` (Option A) is the only expression that represents the correct relationship between the coordinates of R and S.

Let's break down the calculation. If T represents the coordinate of point S, then the measure of segment RS is
`\(T - x\).` In the expression
`\(3x - 4\),` substituting T for x, we get
`\(3T - 4\)`, which is equivalent to
`\(T - x\)` given that
`\(T - x = 3T - 4\). Therefore, \(3x - 4\)`accurately represents the measure of segment RS.

It's essential to understand that the measure of a segment is the absolute difference between the coordinates of its endpoints. In this case, the given expression
`\(3x - 4\)`appropriately captures this relationship, making it the correct representation for the measure of segment RS.

The correct answer is Option A.