If (2, 1), (–1, –2), (3, 3) are the midpoints of the sides BC, CA, AB of a triangle ABC,

Question

If (2, 1), (&ndash;1, &ndash;2), (3, 3) are the midpoints of the sides BC, CA, AB of a triangle ABC, then equation of the line BC is

Accepted Answer

Let D(2, 1), E(−1, −2), F(3, 3) be the midpoints of BC, CA, AB.

By the midpoint theorem, BC is parallel to EF.

Slope of EF = \(\frac{3 - (-2)}{3 - (-1)} = \frac{5}{4}\)

BC passes through D(2, 1) with slope \(\frac{5}{4}\):

\(y - 1 = \frac{5}{4}(x - 2) \Rightarrow 4y - 4 = 5x - 10 \Rightarrow 5x - 4y - 6 = 0\)

Answer: (B)

Question 18