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

Answer:

2/7,-20/7

Step-by-step explanation:

A(-2,-2)and B(2,-5)

Answer 2

Answer:

p( -3/2 , 2)

Step-by-step explanation:

A(-2,0)_______P(x,y)_________________B(0,8)

given:

          x1 = -2       y1 = 0

          x2 = 0       y2 = 8

          x   =  x       y   = y

         4AP =AB ( We will use this equation to calculate m1:m2 )

solution:

Let the required point be P(x,y)

Then, we are given that

4AP = AB

4AP = AP + BP ( As AB can be represented as AP + BP)

$\frac{3AP}{BP}$ = 1

$\frac{AP}{BP} = \frac{1}{3}$   (Considering AP/BP as m1 and m2)

Therefore, m1:m2 = 1:3

Now, By Section Formula, we get:----

x = $\frac{m2x1 + m1x2}{m1 + m2}, y = \frac{m2y1 + m1y2}{m1 + m2}$

putting the values

$x= \frac{(3* -2) + 1*0 }{1 + 3} , y = \frac{3*0 + 1 *8}{1+3}$

$x = \frac{-6}{4} , y = \frac{8}{4}$

$x = \frac{-3}{2} , y = \frac{2}{1}$

$Therefore, P(\frac{-3}{2} ,2)$