Question

Point AAA is at {(2,-8)}(2,−8)left parenthesis, 2, comma, minus, 8, right parenthesis and point CCC is at {(-4,7)}(−4,7)left parenthesis, minus, 4, comma, 7, right parenthesis.

Find the coordinates of point BBB on \overline{AC}
AC
start overline, A, C, end overline such that the ratio of ABABA, B to BCBCB, C is 2:12:12, colon, 1.

Answer 1

The coordinates of point B are (-2, 2).

Explanation:

Given:

Point A (2,−8)

Point C (−4,7)

Point B divides the line AB such that the ratio AB:BC is 2:1.

To find: The coordinates of point B.

Solution:

We can use the segment formula here to find the coordinates of point B which divides line AC in ratio 2:1

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

Where
`(x,y)` is the co-ordinate of the point which

divides the line segment joining the points
`(x_(1), y_(1))` and
`(x_(2), y_(2))` in the ratio
`m:n`.

m = 2

n = 1

As per the given values

`x_(1) = 2\\x_(2) = -4\\y_(1) = 8\\y_(2) = 7`

Putting the values in the formula:

`x = (2 * (-4)+1* 2)/(2+1)=(-8+2)/(3) =-2\\y = (2* 7+1 * (-8))/(2+1) = (6)/(3) =2`

So, the coordinates of point B are (-2, 2).