Q:

Are the points (-4,-1), (2,1) and (11,4) collinear? Justify your answer.

Accepted Solution

A:
Answer: Yes , the points (-4,-1), (2,1) and (11,4) are collinear.Step-by-step explanation:We know that if three points [tex](x_1,y_1),(x_2,y_2)[/tex] and [tex](x_3,y_3)[/tex] are collinear, then their area must be zero.The area of triangle passes through points[tex](x_1,y_1),(x_2,y_2)[/tex] and [tex](x_3,y_3)[/tex] is given by :-[tex]\text{Area}=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]Given points : (-4,-1), (2,1) and (11,4)Then, the area of Ξ”ABC will be :-[tex]\text{Area}=\dfrac{1}{2}|-4(1-4)+(2)(4-(-1))+(11)(-1-1)|\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|-4(-3)+(2)(5)+(11)(-2)||\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|12+10-22|\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|0|=0 [/tex]Hence, the points (-4,-1), (2,1) and (11,4) are collinear.