Question

Let A(2,3) and B(2,-4) be two points. if P lies on the x axis, such that AP = 3/7 AB, Find the coordinates of P?

Answer 1

Given: A(2,3) and B(2,-4) are two points.

P point lies on 'x' axis, therefore the point P is (x,0).

It is given that AP = $\frac{3}{7}$AB

We have to find the coordinates of point P.

Firstly, we will find the distance AP = (2,3) (x,0)

We will use distance formula to find the distance between the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$

Distance AP = $\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

= $\sqrt{(x-2)^{2}+(0-3)^{2}}$

Distance AB = (2,3) (2,-4)

Distance AB = $\sqrt{(2-2)^{2}+(-4-3)^{2}}$ = 7 units

Since  AP = $\frac{3}{7}$AB

So,  $\sqrt{(x-2)^{2}+(0-3)^{2}}$ = $\frac{3}{7} \times$ 7

$\sqrt{(x-2)^{2}+(0-3)^{2}}$ = 3

Squaring on both the sides, we get

$(x-2)^{2}+(0-3)^{2}= 9$

$x^{2}+4-4x+9= 9$

$x^{2}-4x+4= 0$

$x^{2}-2x-2x+4=0$

$x(x-2)-2(x-2)=0$

(x-2)(x-2) = 0

Therefore, x=2.

So, the coordinate P is (2,0).

Answer 2

Answer:

x=2

Step-by-step explanation:

A(2,3) and B(2,-4) are two points.

P point lies on 'x' axis, therefore the point P is (x,0).

It is given that AP = AB

We have to find the coordinates of point P.

Firstly, we will find the distance AP = (2,3) (x,0)

We will use distance formula to find the distance between the points  and  

Distance AP =  

=  

Distance AB = (2,3) (2,-4)

Distance AB =  = 7 units

Since  AP = AB

So,   =  7

= 3

Squaring on both the sides, we get

(x-2)(x-2) = 0

Therefore, x=2.

So, the coordinate P is (2,0).