**Q) The vertices of Δ ABC are A (- 2, 4), B(4, 3) and C(1, – 6). Find length of the median BD.**

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

**Step 1: **To draw median BD, point D lies on AC

Let’s consider the coordinates of D are (X, Y)

Since D is the midpoint of A C, we need to find out the coordinates of D.

We know that the coordinates of mid point of 2 coordinates (X_{1}, Y_{1}) and (X_{2}, Y_{2}) given by:

(X, Y) =

∴ Value of coordinates of midpoint D of A (- 2, 4) and C (1, – 6) are:

(X, Y) =

=

**Step 2:** Next, we find length of BD, where B is (4, 3) and D is (

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 ]}

∴ BD =

=

=

=** 6.02**

**Therefore, the length of the median BD is 6.02 units.**

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