Question

iii. answer the following questions. draw a picture. 9. t is between r and s. rt = 2x, ts = 4, rs = 3x - 1. find rs and rt 10. a basketball coach is interested in measuring a player’s vertical jumping ability. while standing and reaching up, the player’s hand reaches the 4-in. mark on the scale. when jumping, the player can reach the 19-in. mark. what is the player’s vertical jumping ability?

Explanation:

Question 9

Step1: Apply segment addition postulate

Since \( T \) is between \( R \) and \( S \), we have \( RT + TS = RS \). Substituting the given expressions: \( 2x + 4 = 3x - 1 \).

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 4 = x - 1 \). Then add 1 to both sides: \( x = 5 \).

Step3: Find \( RT \) and \( RS \)

For \( RT \): \( RT = 2x = 2(5) = 10 \).
For \( RS \): \( RS = 3x - 1 = 3(5) - 1 = 14 \).

To find the vertical jumping ability, subtract the standing reach from the jumping reach. The standing reach is 4 inches, and the jumping reach is 19 inches. So, \( 19 - 4 = 15 \).

Answer:

\( RT = 10 \), \( RS = 14 \)

Question 10