Determine whether the three points are collinear.
-(5, -1), (-3, 6), (4, -2)
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if three points are collinear, we can use the area of the triangle they form. If the area is 0, the points are collinear. The area of a triangle given three points (x1, y1), (x2, y2), and (x3, y3) can be calculated using the formula: 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. Substituting the given points into this formula gives: 1/2 |5(-6 + 2) + (-3)(-2 + 1) + 4(1 + 6)| = 1/2 |5(-4) - 3(-1) + 4(7)| = 1/2 |-20 + 3 + 28| = 1/2 |11| = 5.5, which is not zero. Therefore, the points are not collinear.

Determine Whether the Three Points Are Collinear