Question

Are the points (5, -2), (-1, 12), and (2, 5) collinear?

A) Yes

B) No

C) Insufficient information

D) Collinearity cannot be determined

Answer 1

The points (5, -2), (-1, 12), and (2, 5) are collinear.

Step-by-step explanation:

To determine if the points (5, -2), (-1, 12), and (2, 5) are collinear, we can calculate the slope between each pair of points. If the slopes are equal, then the points are collinear.

1. Slope between (5, -2) and (-1, 12):
2. Slope = (y2 - y1) / (x2 - x1) = (12 - (-2)) / (-1 - 5) = 14 / -6 = -7/3
3. Slope between (-1, 12) and (2, 5):
4. Slope = (y2 - y1) / (x2 - x1) = (5 - 12) / (2 - (-1)) = -7 / 3

Since the slopes between the points are equal (-7/3), we can conclude that the points are collinear. Therefore, the answer is A) Yes.