Show that the point P(a, b + c), Q(b, c + a) and R(c, a + b) are collinear.

Engineering

Mathematics

Introduction to Determinants

Question

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

P = (a, b + c) = (x₁, y₁)

Q = (b, c + a) = (x₁, y₂)

R = (c, a + b) = (x₃, y₃)

m_pq = slope of $PQ = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$= \frac{c + a - b - c}{b - a}$

$\begin{array}{l} = \frac{a - b}{- (a - b)} \end{array}$

= – 1

m_QR = slope of $\begin{array}{l} QR = \frac{y_{3} - y_{2}}{x_{3} - x_{2}} \end{array}$

$= \frac{a + b - c - a}{c - b}$

$= \frac{b - c}{- (b - c)}$

= – 1

Slope of PQ = slope of QR so points A, B, C are collinear.

Please subscribe our Youtube channel to unlock this solution.