Question

Determine whether the three points are collinear. (3, -10), (-2, -7), (0, -5)

Answer 1

The points are not collinear.

Solution:

Let A, B and C be (3, -10), (-2, -7) and (0, -5).

If slopes of any two points are same, then the points are collinear.

Slope formula:

$m=\frac{y_2-y1}{x_2-x_1}$

Slope of AB:

$m_1=\frac{-7-(-10)}{-2-3}$

$m_1=\frac{-7+10}{-5}$

$m_1=-\frac{3}{5}$

Slope of BC:

$m_2=\frac{-5-(-7)}{0-(-2)}$

$m_2=\frac{-5+7}{2}$

$m_2=\frac{2}{2}$

$m_2=1$

Slope of CA:

$m_3=\frac{-10-(-5)}{3-0}$

$m_3=\frac{-10+5}{3}$

$m_3=-\frac{5}{3}$

$m_1\neq m_2 \neq m_3$

Slope of AB ≠ Slope of BC ≠ Slope of AC

Therefore the points are not collinear.