Question

consider the diagram.
what is qs?
2 units.
5 units.
17 units.
33 units.

Explanation:

Identify the geometric relationship

The diagram shows a line \(l\) that is perpendicular to segment \(RQ\) at point \(T\) (indicated by the right-angle symbol). Additionally, the tick marks on \(RT\) and \(TQ\) indicate that \(RT = TQ\), meaning \(T\) is the midpoint of \(RQ\). Therefore, line \(l\) is the perpendicular bisector of segment \(RQ\). Since point \(S\) lies on line \(l\), by the Perpendicular Bisector Theorem, it is equidistant from the endpoints \(R\) and \(Q\). Thus, we have:

$$RS = QS$$

Set up the equation

Using the Linear Equations knowledge point

$$ 3x + 2 = 5x - 8 $$

Solve for x

Using the Linear Equations knowledge point

$$
LATEXBLOCK0
$$

Calculate the length of QS

Using the Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Answer:

• (A) 2 units.
• (B) 5 units.
• (C) 17 units. (Correct answer)
• (D) 33 units.