Question

Write down the coordinates of a point P that divides the line joining A(-4,1) and B (17,10) Find the equation of the line through P and perpendicular to AB.​

Answer 1

Step-by-step explanation:

● Coordinate geometry ●

A(- 4 , 1) and B(17, 10)

P divides AB in 1 : 2 ratio.

Coordinates of P

$x \: coordinate = \frac{1 \times 17 + 2 \times ( - 4)}{1 + 2} \\ \\ = \frac{17 - 8}{3} \\ \\ = \frac{9}{3} \\ \\ = 3$

And ,

$y \: coordinate = \frac{1 \times 10 + 2 \times 1}{1 + 2} \\ \\ = \frac{10 + 2}{3} \\ \\ = \frac{12}{3} \\ \\ = 4$

Therefore, coordinates of P = ( 3, 4).

Answer 2

Given:-

✯ A(- 4, 1) and B(17, 10)

✯ P divides AB in 1 : 2 ratio.

Solution:-

Coordinates of P

$☞ \: x \: coordinate = \frac{1 \times 17 + 2 \times ( - 4)}{1 + 2} \\ \\ = \frac{17 - 8}{3} \\ \\ = \frac{9}{3} \\ \\ = 3$

$☞ \: y \: coordinate = \frac{1 \times 10 + 2 \times 1}{1 + 2} \\ \\ = \frac{10 + 2}{3} \\ \\ = \frac{12}{3} \\ \\ = 4$

Therefore, coordinates of P are ( 3, 4).