Determine if the points (1,5), (2,3), and (-2 | vedclass

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(B) Let the points be $A(1,5), B(2,3),$ and $C(-2,-11)$.To check if the points are collinear,we calculate the area of the triangle formed by these poi

Vedclass · Accepted Answer

No,they are not collinear.

Vedclass · Answer

(B) Let the points be $A(1,5), B(2,3),$ and $C(-2,-11)$.To check if the points are collinear,we calculate the area of the triangle formed by these points using the formula:$	ext{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$Substituting the values:$	ext{Area} = \frac{1}{2} |1(3 - (-11)) + 2(-11 - 5) + (-2)(5 - 3)|$$	ext{Area} = \frac{1}{2} |1(14) + 2(-16) + (-2)(2)|$$	ext{Area} = \frac{1}{2} |14 - 32 - 4|$$	ext{Area} = \frac{1}{2} |-22| = 11 	ext{ square units}$.Since the area of the triangle is not $0$,the points are not collinear.

Determine if the points $(1,5), (2,3),$ and $(-2,-11)$ are collinear.

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