Question

Given the points A(-3,-4) and B(2,0), point P(-1,-12/5) partions AB in the ratio

Answer 1

2:3

Explanation:

Given: Points A(-3,-4) and B(2,0), point P(-1,-12/5)

To find: The ratio in which P divide AB

Solution:

We know that the coordinate of a point
`(x,y)` dividing a line segment joining
`(x_(1),y_(1)) \:\text{and} (x_(2),y_(2))` in the ratio m:n is given by

`x=(mx_(2)+nx_(1))/(m+n)`,
`y=(my_(2)+ny_(1))/(m+n)`

Now, let the ratio be k:1

Here, coordinate of P is
`(-1,(-12)/(5) )`

So,
`-1=( k(2)+1(-3))/(k+1)`

`-k-1=2k-3`

`2k+k=3-1`

`3k=2`

`k=(2)/(3)`

Hence, the ratio is 2:3.

Answer 2

The x-coordinate of P (-1) is 2 units from that of A and 3 units from that of B.

P partitions AB in the ratio 2:3.