Question

If the abscissa of a point P is 2, find the ratio in which this point divides the line segment joining the point (−4, 3) and (6, 3). Also, find the co-ordinates of point P.

Answer 1

Abscissa of a point P is 2

Let co-ordinates of point P be (2, y)

Let point P(2, y) divides the line segment joining the points (−4, 3) and (6, 3) in the ratio

`k : 1{x = (kx_2 + 1*x_1)/(k + 1)}`

∴ `2 = (6k - 4)/(k + 1)`

`=>` 2k + 2 = 6k – 4

`=>` 6k – 2k = 2 + 4

`=>` 4k = 6

`=> k = 6/4 = 3/2`

∴ Required ratio be 3 : 2

Now, `y = (ky_2 + 1*y_1)/(k + 1)`

= `(3k + 3)/(k + 1)`

= `(3 xx 3/2 + 3)/(3/2 + 1)`

= `(9/2 + 3)/(3/2 + 1)`

= `((9 + 6)/2)/((3 + 2)/2)`

= `(15/2)/(5/2)`

= `15/2 xx 2/5`

= 3

∴ Co-ordinates of point P are (2, 3).