Question

If A and B are two points having coordinates (–2, –2) and (2, –4) respectively, find the coordinates of P such that `AP = 3/7 AB`. Also, find the coordinates of P on AB such that `BP = 4/7 AB`.

Answer 1

We have two points A (–2, –2) and B (2, –4). Let P be any point which divide AB as,

`AP = 3/7 AB`

Since,

`AB = (AP + BP)`

So,

7AP = 3AB

7AP = 3(AP + BP)

4AP = 3BP

`(AP)/(BP) = 3/4`

Now according to the section formula if any point P divides a line segment joining `A(x_1,y_1)` and `B(x_2,y_2)` in the ratio m : n internally than,

`P(x, y) = ((nx_1 + mx_2)/(m + n), (ny_1 + my_2)/(m + n))` 

Therefore P divides AB in the ratio 3 : 4. So,

`P(x, y) = ((3(2) + 4(-2))/(3 + 4), (3(-4) + 4(-2))/(3 + 4))`

= `(-2/7, -20/7)`