Question

Find the Coordinates of a point P which lies on the line segment joining points A(-2,0) and B(0,8) such that 4AP=AB .​

Answer 1

Given:

A(-2,0) and B(0,8)

and 4AP = AB

⇒AP=$\frac{1}{4}$AB

If we will visualize this on a line It will look like this:

    ____p(x,y)____________B(0,8)

A(-2,0)

clearly P is diving AB in the ratio 1:3

(as we have 4 parts of AB)

so, m1:m2 = 1:3

to find:

coordinates of P

Solution:

Let, the required Point be in the form P(x,y).

now,

x1= -2 , y1 = 0

x2= 0 , y2 = 8

x = x   , y   = y

m1 = 1 , m2 = 3

Now , by section Formula ,we get:-

First solving for x:

$x = \frac{m1x2 + m2x1}{m1 + m2}$

Substituting the values

$x = \frac{1*0+ 3*-2}{1 + 3}$

$x = \frac{-6}{4}$

$x = \frac{-3}{2}$ [value of x]

Now solving for y:

$y = \frac{m1y2 + m2y1}{m1 + m2}$

substituting the values

$y = \frac{1*8 + 3*0}{1 + 3}$

$y = \frac{8}{4}$

$y = 2$[value of y]

therefore the required point P will be

P(-3/2 , 2)

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Answer 2

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