Question

If \( P(0,0) \), \( Q(8,0) \) and \( R(0,12) \) are the vertices of \( \triangle PQR \), then the area of \( \triangle PQR \) is:

• A. \(40\)
• B. \(48\)
• C. \(20\)
• D. \(4\)

Hint:

When two vertices lie on the axes and the third is the origin, the triangle is right-angled at the origin; use \(\tfrac{1}{2}\times (\text{x-intercept})\times(\text{y-intercept})\).

Answer 1

The Correct Option is B

Step 1: Observe the triangle is right-angled on the axes.
Points \(Q(8,0)\) and \(R(0,12)\) lie on the coordinate axes, with \(P(0,0)\) at the origin. Hence, \(PQ\) is along the \(x\)-axis with length \(8\) and \(PR\) is along the \(y\)-axis with length \(12\).
Step 2: Use area formula for a right triangle.
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times 12 = 48. \]
Step 3: Conclude.
Therefore, the area of \( \triangle PQR \) is \(48\).