Question

With the help of distance formula , show that the points P ( a , b + c ) , Q ( b , c + a ) and R (c , a + b ) are collinear points​

Answer 1

$P(a,b+c)=(x1,y1) \\ Q=(b,c+a)=(x1,y2) \\ R=(c,a+b)=(x3,y3) \\ m(pq)=slope \: of \: PQ= \frac{y2 - y1}{x2 - x1} \\ = \frac{c + a - b - c}{b - a} \\ = \frac{a - b}{b - a}\\ = \frac{a - b}{- (a - b)} \\ - = - 1 \\ m(qr)=slope \: of \: QR= \frac{y3 - y2}{x3 - x2} \\ = \frac{a + b- c - a}{c - b} \\ = \frac{b - c}{c - b} \\ = \frac{b - c}{- (b - c)} \\ = - 1$

Slope of PQ=Slope of QR

Therefore, P ( a , b + c ) , Q ( b , c + a ) and R (c , a + b ) are collinear points