Question

1. Write down the co-ordinates of the point P that divides the line joining A(−4, 1) and B(17, 10) in the ratio 1 : 2.
2. Calculate the distance OP, where O is the origin.
3. In what ratio does the y-axis divide the line AB?

Answer 1

i. Co-ordinates of point P are

`((1 xx 17 + 2 xx (-4))/(1 + 2),(1 xx 10 + 2 xx 1)/(1 + 2))`

= `((17 - 8)/3, (10 + 2)/3)`

= `(9/3, 12/3)`

= (3, 4)

ii. `OP = sqrt((0 - 3)^2 + (0 - 4)^2)`

`OP = sqrt(9 + 16)`

`OP = sqrt(25)`

OP = 5 units

iii. Let AB be divided by the point P(0, y) lying on y-axis in the ratio k : 1

∴ `(0, y) = ((k xx 17 + 1 xx (-4))/(k + 1),(k xx 10 + 1 xx 1)/(k + 1))`

`=> (0, y) = ((17k - 4)/(k + 1),(10k + 1)/(k + 1))`

`=> 0 = (17k - 4)/(k + 1)`

`=> 17k - 4 = 0`

`=> k = 4/17`

Thus, the ratio in which the y-axis divide the line AB is 4 : 17.