Question

a point A on x-axis,point B on y-axis and point P lies on line segment AB ,such that P(4,5) and AP:BP=5:3. find the coordinates of points A and B.

Answer 1

let coordinates of A = (a,0)
and coordinates of B = (0,b)
and coordinates of are = (4,5)

so, 4 = 3a+0/8
a = 32/3
5 = 5b+0/8
40/5 = b
b = 8 cm ans.

Answer 2

Answer:

$A=(\frac{32}{3},0)$

$B=(0,8)$

Step-by-step explanation:

Given: A point A on x-axis,point B on y-axis and point P lies on line segment AB ,such that P(4,5) and AP:BP=5:3.

To find : The coordinates of points A and B.

Solution :  

Let point $P(x_3,y_3)=(4,5)$ divides  the line segment joining the points $A(x_1,y_1)=(a,0)$ and point $B(x_2,y_2)=(0,b)$  in ratio AP:BP=5:3

Then, Using section formula,

$(x_3,y_3)=\frac{x_1n+x_2m}{m+n},\frac{y_1n+y_2m}{m+n}$

$(4,5)=(\frac{3a+0(5)}{5+3}),(\frac{0(3)+b(5)}{5+3})$  

$(4,5)=(\frac{3a}{8}),(\frac{5b}{8})$  

Equating x-coordinate,

$4=\frac{3a}{8}$  

$4\times 8=3a$  

$32=3a$  

$a=\frac{32}{3}$  

Equating y-coordinate,

$5=\frac{5b}{8}$  

$5\times 8=5b$  

$40=5b$  

$a=\frac{40}{5}$  

$a=8$  

Therefore, Point A and B are

$A=(a,0)=(\frac{32}{3},0)$

$B=(0,b)=(0,8)$