Find the length of the median AD of Δ ABC having vertices

Q) Find the length of the median AD of Δ ABC having vertices A(0, –1), B(2, 1) and C(0, 3).

Ans: Let’s plot the points on the graph:

Step 1: Let’s understand the layout:

If AD is median, it means D lies on line segment BC, and BD = CD

Let the coordinates of point D be (x, y)

We know that the coordinates of midpoint of 2 coordinates (X₁, Y₁) and (X₂, Y₂) given by:

(X, Y) = $(\frac{(X_1 + X_2)}{2}, \frac{(Y_1 + Y_2)}{2})$

∴ value of coordinates of midpoint D of B (2, 1) and C(0, 3) are:

(X, Y) = $(\frac{(2 + 0)}{2}, \frac{(1 + 3)}{2})$

= $(\frac{2}{2}, \frac{4}{2})$

= (1, 2)

Step 2: Next, we find out the length of line AD, where A is (0, – 1) and D is (1, 2)

We know that the distance between two points (X₁, Y₁) and (X₂, Y₂) is given by:

S = √ [(X₂ – X₁)² + (Y₂ – Y₁)^{2 ]}

∴ AD = $\sqrt{(1 - 0)^2 + (2 - (- 1)^2}$

= $\sqrt{(1 + 9)}$

= √ 10 units

Therefore, the length of the median AD is √10 units.

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