Question

If P (1, 2), Q (3, 5), R (7, 9) form a triangle then find the equation of median through P.

(a) 5x-4y+3 = 0

(b) 5x+4y+3 = 0

(c) 5x-4y-3 = 0

(d) 5x+4y-3 = 0

The question was posed to me by my college director while I was bunking the class.

I would like to ask this question from General Equation of a Line in division Straight Lines of Mathematics – Class 11

Answer 1

Correct option is (a) 5x-4y+3 = 0

The best I can explain: Midpoint of QR line is \((\frac{3+7}{2}, \frac{5+9}{2})\) = (5, 7).

Equation of line joining (1, 2) and (5, 7) is \(\frac{y-2}{7-2} = \frac{x-1}{5-1}\)

=>\(\frac{y-2}{5} = \frac{x-1}{4}\) => 4y-8 = 5x-5 => 5x-4y+3 =0.