Question:
In ∆ABC, ∠B is a right angle, AC = 6 cm, and D is the mid-point of AC. The length of BD is
In ∆ABC, ∠B is a right angle, AC = 6 cm, and D is the mid-point of AC. The length of BD is
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In geometry, assign coordinates to simplify right-angle triangle and midpoint calculations.
Updated On: Jul 24, 2025
- 3 cm
- 4 cm
- 5 cm
- 2√2 cm
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The Correct Option is C
Solution and Explanation
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
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
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