Question

Find the coordinates of P so that P partitions the segment AB in the ratio 6:2 if A(−4,12) and B(9,−4).

A. (13.75, -24)
B. (5.75, 0)
C. (-16, 13)
D. (9.75, -12)

Answer 1

B. (5.75, 0)

Step-by-step explanation

If the point P(x,y) partitioned

`A(x_1,y_1)`

and

`B(x_2,y_2)`

in the ratio m:n, then

`x = (mx_2+nx_1)/(m + n)`

`y=(my_2+ny_1)/(m + n)`

If the coordinates are A(−4,12) and B(9,−4), then:

`x = (6 * 9+2 * - 4)/(6 + 2)`

`x = (54 - 8)/(8)`

`x = (46)/(8)`

`x = 5.75`

`y= (6 * - 4+2 * 12)/(6 + 2)`

`y = (24 - 24)/(8)`

`y = (0)/(24) = 0`

The correct choice is

`B. (5.75, 0)`