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

Answer:

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

Step-by-step 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

$x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}$

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:

$x = \dfrac{2 \times (-4)+1\times 2}{2+1}=\dfrac{-8+2}{3} =-2\\y = \dfrac{2\times 7+1 \times (-8)}{2+1} = \dfrac{6}{3} =2$

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