If points (t, 2t), (-2, 6) and (3, 1) are collinear, then t is equal to Option 1: 3/4 Option 2: 4/3 Option 3: 3/5 Option 4: 5/3

For collinear points, area of triangle formed by these points should be zero. area formula: 1/2|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = 0 are: (t,2t), (-2,6), (3,1)1/2|t(6 - 1) + (-2)(1 - 2t) + 3(2t - 6)| = 01/2|5t + (-2 + 4t) + (6t - 18)| = 01/2|5t + (-2 + 4t) + (6t - 18)| = 01/2|15t - 20| = 0|15t - 20| = 015t - 20 = 015t = 20 = 4/3, t = 4/3

JIPMAT 2021 (QA) - If points (t, 2t), (-2, 6) and (3, 1) are collinear, then t is equal to | PYQs + Solutions

JIPMAT 2021

Geometry

Coordinate Geometry

Conceptual

If points $(t, 2t)$ , $(-2, 6)$ and $(3, 1)$ are collinear, then $t$ is equal to

\frac{3}{4}

\frac{4}{3}

\frac{3}{5}

\frac{5}{3}

Correct Option: 2

For collinear points, area of triangle formed by these points should be zero.

Using area formula:

\frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = 0

Points are:

(t,2t), (-2,6), (3,1)

\frac{1}{2}|t(6 - 1) + (-2)(1 - 2t) + 3(2t - 6)| = 0

\frac{1}{2}|5t + (-2 + 4t) + (6t - 18)| = 0

\frac{1}{2}|5t + (-2 + 4t) + (6t - 18)| = 0

\frac{1}{2}|15t - 20| = 0

|15t - 20| = 0

15t - 20 = 0

15t = 20

t = \frac{4}{3}

Therefore,

t = \frac{4}{3}

JIPMAT 2021 (QA) PYQs

If points (t,2t)(t, 2t)(t,2t), (−2,6)(-2, 6)(−2,6) and (3,1)(3, 1)(3,1) are collinear, then ttt is equal to

Keyboard Shortcuts

If points $(t, 2t)$ , $(-2, 6)$ and $(3, 1)$ are collinear, then $t$ is equal to