Question

In ∆ABC, ∠B is a right angle, AC = 6 cm, and D is the mid-point of AC. The length of BD is

• A. 3 cm
• B. 4 cm
• C. 5 cm
• D. 2√2 cm

Hint:

In geometry, assign coordinates to simplify right-angle triangle and midpoint calculations.

Answer 1

The Correct Option is C

Step 1: ∆ABC is right-angled at B. Use coordinate geometry. Let’s assign:
A = (0, 0), C = (6, 0) so that AC = 6 cm.
Step 2: To ensure ∠B = 90°, place B at (0, 4).
Step 3: Mid-point D of AC = ((0+6)/2, (0+0)/2) = (3, 0)
Step 4: Use distance formula to find BD:
BD = √[(3−0)² + (0−4)²] = √[9 + 16] = √25 = 5 cm