Question

if (3,2) (-3,5) and (x,y) are collinear, show that x+2y-7=0​

Answer 1

If they are collinear they must have same slope(or you can say, they lie on the same line).

Slope of (3,2) and (-3,5) = slope of (3, 2) and (x, y)

⇒ (5 - 2)/(-3 - 3) = (y - 2)/(x - 3)

⇒ 3/(-6) = (y - 2)/(x - 3)

⇒ -1/2 = (y - 2)/(x - 3)

⇒ -(x - 3) = 2(y - 2)

⇒ - x + 3 = 2y - 4

⇒ 0 = x + 2y - 7           proved.

       Method 2:

As they lie on the same line, they must satisfy the equation of line.

 Slope of line = (5-2)/(-3-3) = -1/2

Therefore, equation of line is:

⇒ (y - y₁) = m(x - x₁)

⇒ y - 2 = (-1/2)(x - 3)

⇒ 2y - 4 = -(x - 3)

⇒ x + 2y - 7 = 0        proved