divide line segments

Question

Point A is at (-6,-5) and point C is at (4,0)

Find the coordinates of point of B on AC such that the ratio of AB to BC is 2:3

Answer 1

Let (a,b) be the point

As we move along the line segment from (-6,-5) to (4,0), x increases by 10 and y increases by 5.

So, a = -6 + (2/5)(10) = -2 and b = -5 + (2/5)(5) = -3

(a,b) = (-2, -3)

Answer 2

A(-6,-5) C(4,0)

divide into ratio of 2:3

that point B is (-2, -3)

find 2/(2+3) = 2/5 of the way up the line

2/5 x (4--6) +-6 = -2

2/5 x (0--5) + -5= -3

helps to plot the points and graph the line