Question

The point P (5, -4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5. Find the coordinates of points A and B.

Answer 1

Let the A be (x,0)

And B be (0,y)

Mid point of AB = Co ordinats

Use section formula

Use this and do

Answer 2

The coordinates of points A and B are (7,0) and (0,-14).

Step-by-step explanation:

Point A lies on x-axis, so coordinates of point A are (a,0).

Point B lies on y-axis, so coordinates of point A are (0,b).

It is given that the point P (5, -4) divides the line segment AB, as shown in the figure, in the ratio 2 : 5.

Section formula:

If a point divides a line segment in m:n whose end points are and , then the coordinates of that point are

$(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})$

Using section formula the coordinates of point P are

$P=(\dfrac{(2)(0)+(5)(a)}{2+5},\dfrac{(2)(b)+(5)(0)}{2+5})$

$P=(\dfrac{5a}{7},\dfrac{2b}{7})$

It is given that point P is at (5, -4).

$(5,-4)=(\dfrac{5a}{7},\dfrac{2b}{7})$

On comparing both sides we get

$\dfrac{5a}{7}=5\Rightarrow a=7$

$\dfrac{2b}{7}=-4\Rightarrow -14$

Therefore, the coordinates of points A and B are (7,0) and (0,-14).

#Learn more

Divides seg AB in the ratio 2:1, if A (-6,10) and B (-3,4). Find the

co-ordinates of point P.

​https://brainly.in/question/14125406