Question

Point A is at (-6,-5) and point C is at (4,0) . Find the coordinates of point B on AC such that the ratio of AB to BC is 2: 3

Answer- B=(?,?)

Answer 1

B = (-2,-3)

Explanation:

Here, we are to split a the length of a line in a particular ratio.

The ratio we are to split in is the ratio 2:3

Now, the formula to use for the points of the splitted ratio is

x = (bx1 + ax2) / (a ​​+ b)

y = (by1 + ay2) / (a ​​+ b)

where (x1,y1) = (-6,-5) and (x2,y2) = (4,0)

while a and b = 2 and 3

Now substituting these values, we have

x-point = {3(-6) + 2(4)}/(2+3) = (-18+8)/5 = -10/5 = -2

y-point = {3(-5) + 2(0)/(2+3) = (-15+0)/5 = -15/5 = -3

The coordinates of the point B is thus (-2,-3)