Question

without using distance formula prove that points A(1,4), B(3,-2) , and C(-3,16) are collinear .​

Answer 1

Step-by-step explanation:

If A, B and C are collinear, their slopes must be equal.

Slope of any two point is given by $(\small{\frac{y_2-y_1}{x_2-x_1}}$

Using this, if both are collinear:

Slope of AB = $\small{\frac{-2-4}{3-1}} =\small{\frac{-6}{2}} =-3$

Slope of BC = $\small{\frac{-2-16}{3-(-3)}} =\small{\frac{-18}{6}} =-3$

As both the slopes are equal, these points are collinear.

Answer 2

Answer:

If A, B and C are collinear, their slopes must be equal.

Slope of any two point is given by (\small{\frac{y_2-y_1}{x_2-x_1}}(x2−x1y2−y1

Using this, if both are collinear:

Slope of AB = \small{\frac{-2-4}{3-1}} =\small{\frac{-6}{2}} =-33−1−2−4=2−6=−3

Slope of BC = \small{\frac{-2-16}{3-(-3)}} =\small{\frac{-18}{6}} =-33−(−3)−2−16=6−18=−3

As both the slopes are equal, these points are collinear.