Question

Points $(1,5),(2,3)$ and $(-2,-11)$ are ____

• A. Non-collinear
• B. Collinear
• C. Vertices of equilateral triangle
• D. Vertices of right angle triangle

Answer 1

The correct option is A Non-collinear

Use the distance formula to find out $l_1$, $l_2$ and $l_3$
$l=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
$l_1=\sqrt{{(2-1)}^2+{(3-5)}^2}=\sqrt{1+4}=\sqrt{5}{l}_2=\sqrt{{(-2-2)}^2+{(-11-3)}^2}=\sqrt{16+196}=\sqrt{212}{l}_3=\sqrt{{(1+2)}^2+{(5+11)}^2}=\sqrt{9+256}=\sqrt{265}$
$l_1=\sqrt{5}$, $l_2=\sqrt{212}$ and $l_3=\sqrt{265}$
Points will be co-linear, if length of one side equals the linear combination of length of other two sides.
Since $l_3\ne l_2+l_1$,
Points are non collinear.