Question

Can u draw a triangle with vertices (1,5) (5,8) and(13,14) . Give reasons?

Answer 1

$(1,5) = (x_ 1,y_1 )$
$(5,8) = (x_2,y_2)$
$(13,14) = (x_3,y_3)$

Area of a triangle = $\frac{1}{2} | (x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2) |$
= $\frac{1}{2} | 1(8-14) + 5(14-5) + 13(5-8) |$
= $\frac{1}{2} | 1(-6) + 5(9) + 13(-3) |$
= $\frac{1}{2} | -6 + 45 - 39 |$
= $\frac{1}{2} | 45 - 45 |$
= $\frac{1}{2} | 0 |$
= $\frac{0}{2}$ = 0

The area of the triangle is equal to zero. So we can not form a triangle.
The given points are collinear