Question

If area of triangle is 35 sq. units with vertices \( (2,-6), (5,4) \) and \( (k,4) \), then \( k \) is _____

• A. \( 12 \)
• B. \( -12, -2 \)
• C. \( -2 \)
• D. \( 12, -2 \)

Hint:

Always use determinant formula for area of triangle in coordinate geometry.

Answer 1

The Correct Option is D

Concept: Area of triangle: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) \right| \]
Step 1: Substitute points. \[ \frac{1}{2} |2(4-4) + 5(4+6) + k(-6-4)| = 35 \]
Step 2: \[ \frac{1}{2} |0 + 50 - 10k| = 35 \] \[ |50 - 10k| = 70 \]
Step 3: \[ 50 - 10k = \pm 70 \] \[ k = -2 \quad \text{or} \quad 12 \]