**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 (X_{1}, Y_{1}) and (X_{2}, Y_{2}) given by:

(X, Y) =

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

(X, Y) =

=

= (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 (X_{1}, Y_{1}) and (X_{2}, Y_{2}) is given by:

S = **√ **[(X_{2} – X_{1})^{2 } + (Y_{2} – Y_{1})^{2 ]}

∴ AD =

=

=** √ 10 units**

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

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