Question

If the coordinates of the sides AB and AC of ∆ABC are (3, 5) and (−3, −3), respectively, then write the length of side BC.

Answer 1

Disclaimer: In the question it should have been the coordinates of the mid points of AB and AC are (3, 5) and ($-$3, $-$3)

Given: the coordinates of the midpoints of AB and AC are (3,5) and ($-$3, $-$3).
Let, D and E be the midpoints of AB and AC, respectively.

$$\begin{gathered} \therefore DE=\sqrt{{\left[3-\left(-3\right)\right]}^2+{\left[5-\left(-3\right)\right]}^2} \\ =\sqrt{6^2+8^2} \\ =\sqrt{100} \\ =10\mathrm{units} \end{gathered}$$

Now, as D and E are midpoints of AB and AC respectively,
by the mid-points theorem,

$$\begin{gathered} BC=2\times DE \\ =2\times 10\mathrm{units} \\ =20\mathrm{units} \end{gathered}$$