Question

solve these questions ​

Answer 1

Answer:

The value of p is 5

Step-by-step explanation:

There are many ways to solve the problem. I am going with slope method

If points (2, 1), (p, -1) and (-1, 3) are collinear then

The slope of line joining (2, 1) and (-1, 3) will be equal to the slope of line joining points (p, -1) and (-1, 3)

We know that slope of line joining the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by

$\boxed{m=\frac{y_2-y_1}{x_2-x_1}}$

Therefore, the slope of line joining the points (2, 1) and (-1, 3)

$=\frac{3-1}{-1-2} =-\frac{2}{3}$

Slope of line joining the points (p, -1) and (-1, 3)

$=\frac{3+1}{-1-p}=-\frac{4}{p+1}$

Both the slopes will be equal

Thus

$-\frac{2}{3}=-\frac{4}{p+1}$

$\implies \frac{1}{3}=\frac{2}{p+1}$

$\implies p+1=6$

$\implies p=5$