Question

Question 20 By using the concept of equation of a line, prove that the three points (3, 0), (–2, –2) and (8, 2) are collinear.

Class X1 - Maths -Straight Lines Page 220

Answer 1

Let the Given points are
P(3,0)
Q(-2,-2)
R(8,2)

Now, equation of line PQ is
(y -y1) =(y2-y1)/(x2-x1)(x-x1)
here,
(x1,y1) = (3,0)
(x2,y2) =(-2,-2)

(y -0) = (-2-0)/(-2-3)(x-3)
y = {-2/-5}(x -3)
5y = 2(x - 3)
2x - 5y - 6 = 0-----(1)

put the point R (8,2) in equation (1),we get

2 × 8 - 5 × 2 - 6 = 0
16 - 10 - 6 = 0
16 - 16 = 0
0 = 0

Hence, Points P, Q, R are collinear.