Questions: Let R, S, T be points on a line with coordinates -7,5, and x respectively. Find the possible coordinate(s) of T if RS=3 RT.

Transcript text: Let $R, S, T$ be points on a line with coordinates $-7,5$, and $x$ respectively. Find the possible coordinate(s) of $T$ if $R S=3 R T$.

Solution

Solution Steps

Step 1: Understand the Problem

We are given three points $ R, S, T $ on a line with coordinates $-7, 5$, and $ x $ respectively. We need to find the possible coordinate(s) of $ T $ such that the distance $ RS = 3RT $.

Step 2: Set Up the Equation

The distance between two points on a line is the absolute difference of their coordinates. Therefore, the distance $ RS $ is:

\[ RS = |5 - (-7)| = |5 + 7| = 12 \]

The distance $ RT $ is:

\[ RT = |x - (-7)| = |x + 7| \]

According to the problem, $ RS = 3RT $. Therefore, we have:

\[ 12 = 3|x + 7| \]

Step 3: Solve the Equation

Divide both sides of the equation by 3:

\[ |x + 7| = 4 \]

This absolute value equation gives us two possible cases: