Question

A line passes through the points A(-3,-2) and B(2,1). Does it also pass through the point C(5,3)? Justify your conclusion.

Answer 1

Given info : A line passes through the points A(-3, -2) and B(2, 1).

To check : does it pass through the point C(5, 3) ?

Also we have to justify our conclusion.

Solution : first find equation of line passing through point A(-3, -2) and B(2, 1),

slope of line = (-2 - 1)/(-3 - 2) = -3/-5 = 3/5

so equation of line,

(y - 1) = 3/5 (x - 2)

⇒5(y - 1) = 3(x - 2)

⇒5y - 5 = 3x - 6

⇒3x - 5y - 1 = 0

Now check point C(5, 3) satisfies or not,

3(5) - 5(3) - 1 = -1 ≠ 0

So, point C (5, 3) doesn't not satisfy equation of line 3x - 5y - 1 = 0, so point C doesn't lie on the line.

Therefore the line passing through the point A and B , doesn't pass through the point C.