Question

4. If the points (1,-1), (2, 3) and (p, 0) are collinear, find p. 1894​

Answer 1

Answer:

$\large\bold\red{p=1}$

Step-by-step explanation:

Given,

(1, -1) , (2, 3) and (p, 0) are 3 collinear points.

We know that,

A triangle formed by collinear points has an area equal to zero square units.

Also,

we know that,

Area formed by 3 points, (a, b) , (c, d) and (e, f) is given by,

$= \bold{\frac{1}{2} |a(d - f) - b(c - e) + 1(cf - de)| }$

Therefore,

in the given condition,

we have,

Area = 0

$= > \frac{1}{2} |1(3 - 0) - ( - 1)(2 - p) + 1(0 - 3p)| = 0 \\ \\ = > |1 \times 3 + 1(2 - p) + 1 \times ( - 3p)| = 0 \\ \\ = > |3 + 2 - 2p - 3p| = 0 \\ \\ = > |5 - 5p| = 0 \\ \\ = > 5 |1 - p| = 0 \\ \\ = > |1 - p| = 0 \\ \\ = > 1 - p = 0 \\ \\ = > p = 1$

Hence,

$\large\bold{p=1}$