Question

Point A is at (6,-6) and point C is at (-6,-2). Find the coordinates of point B on line AC such that AB= 3/4 AC Urgent, need this immediately. PLS EXPLAIN

Answer 1

(-3,0)..................

Answer 2

`B(x,y) = (-3,0)`

Explanation:

Given

`A = (6,-6)`

`C = (-6,2)`

`AB = (3)/(4) AC`

Required

Find coordinates of B

First, we need to convert
`AB = (3)/(4) AC` to ratio
`AB:BC`

SInce
`AB = (3)/(4) AC`, then

`AB : BC = 3 : 4 - 3`

`AB : BC = 3 : 1`

The coordinates of B can then be calculated as follows;

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

Where

`A(x_1,y_1) = A(6,-6)`

`C(x_2,y_2) = A(-6,2)`

`m:n = 3 : 1`

Substitute these values in the given formula;

`B(x,y) = ((1 * 6 + 3 * -6)/(1 + 3),(1 * -6 + 3 * 2)/(1 + 3))`

`B(x,y) = ((6 -18)/(4),(-6 + 6)/(4))`

`B(x,y) = ((-12)/(4),(0)/(4))`

`B(x,y) = (-3,0)`

Hence, the coordinates of B is
`(-3,0)`