Find the length of the median through $A$ of $\Delta ABC$ with vertices $A(7, -3), B(5, 3)$ and $C(3, -1)$.
Step-by-Step Solution
Key Concept: Midpoint $D$ of $BC = \left(\dfrac{5+3}{2}, \dfrac{3-1}{2}\right) = (4, 1)$. Length $AD = \sqrt{(7-4)^2 + (-3-1)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.
Midpoint of $BC$, $D = \left(\dfrac{8}{2}, \dfrac{2}{2}\right) = (4, 1)$. [1.0 Mark]
Length $AD = \sqrt{(7 - 4)^2 + (-3 - 1)^2} = \sqrt{9 + 16} = 5$. [1.0 Mark]
---
🎯 Official CBSE Marking Scheme:
Finding midpoint $D(4, 1)$: 1.0 Mark
Calculating distance $AD = 5$: 1.0 Mark
Correct Answer: