Find y such that the points are collinear.
(5,-4), (3,y), (4,-3)

A)y = -2
B)y = 1
C)y = 0
D)y = -1
E)y = 2

Question

Find y such that the points are collinear. ​
(5,-4), (3,y), (4,-3)
​
A)y = -2
B)y = 1
C)y = 0
D)y = -1
E)y = 2

Quizplus · Accepted Answer

The points are collinear if the area of the triangle formed by them is zero. The area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by the formula:Area = 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|Substituting the given values into the formula, we get:Area = 1/2 |5(-4 - y) + 3(y - (-3)) + 4((-3) - (-4))|= 1/2 |5(-4 - y) + 3(y + 3) + 4(-1)|= 1/2 |-20 - 5y + 3y + 9 - 4|= 1/2 |-16 - 2y|For the points to be collinear, the area of the triangle must be zero. Therefore, we have:|-16 - 2y| = 0-16 - 2y = 0 or -16 - 2y = 0-2y = 16 or -2y = -16y = -8 or y = 8Since y cannot be equal to -8, the only possible value of y is y = -8. Therefore, the correct answer is A) y = -2.

Find Y Such That the Points Are Collinear