Line segment AC has endpoints A(-0.2, -0.7) and C(1, -0.2). Point B is on line segment AC and is located at B(0.04, -0.6). What is the ratio of AB/AC?

Question

Line segment AC has endpoints A(-0.2, -0.7) and C(1, -0.2). Point B is on line segment AC and is located at B(0.04, -0.6). What is the ratio of AB/AC?

Answer 1

This problem is easiest when visualized. Your given lines are AC and AB. Create a right triangle with new point D at (-2,-.2)

Also create point E at (-.2,-.6) as shown. This line is by definition parallel to DC.

By subtraction, the length of DC is 1.2

Also by subtraction, the length of EB is 0.24.

The ratio of these two segments is .24/1.2= 0.2

By theorem, the two triangles you have created are similar, which likewise tells us that the ratio of the hypotenuse AB of the small triangle AEB is in like proportion to the hypotenuse AC of the large triangle ADC.

Therefore, if EB/DC = 0.2, then AB/AC also = 0.2

Answer 2

If A(a,b) and B(c,d) are the co-ordinates of a line segment, then

[a(1-p)+pb,c(1-p)+dp] are the co-ordinates of the point which divides the segment into pieces in ratio p:(1-p), where 0<p<1.

You should use this information to solve your problem where p=.2.