Question

Point AAA is at {(-6,-5)}(−6,−5)left parenthesis, minus, 6, comma, minus, 5, right parenthesis and point CCC is at {(4,0)}(4,0)left parenthesis, 4, comma, 0, 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 2:32:32, colon, 3.

Answer 1

Answer:

B(-2,-3).

Step-by-step explanation:

The given points are A(-6,-5) and C(4,0).

We need to find the coordinates of point B on segment AC such that AB:BC=2:3.

It means point B divides the line segment AC in the ratio of 2:3.

Section formula: If a point divide a line segment in m:n, then

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)$

Using section formula, the coordinates of point B are

$B=\left(\dfrac{2(4)+3(-6)}{2+3},\dfrac{2(0)+3(-5)}{2+3}\right)$

$B=\left(\dfrac{8-18}{5},\dfrac{0-15}{5}\right)$

$B=\left(\dfrac{-10}{5},\dfrac{-15}{5}\right)$

$B=\left(-2,-3\right)$

Therefore, the coordinates of point B are (-2,-3).

Answer 2

Answer:

Therefore, the coordinates of point B are (-2,-3).

Step-by-step explanation: