In what ratio does the x-axis divide the segment joining (-5,4) and (4,-8)?

Question

i need to find the ratio of the x-axis that divides the segment joining (-5; 4) and (4;-8)

Answer 1

The graph below should make the answer clear:

AB is the line joining the given points. The lengths of the sides of the large right triangle can be seen.

AC=4-(-8)=12 units, BC=4-(-5)=9 units.

We have two similar triangles AED and ABC. AD/AC=DE/BC=AE/AB, so AE/AB=AD/AC.

AD is the y-coordinate of A=4, AC=12, so AE/AB=4/12=⅓. All the dimensions of the small right triangle are a third of the large triangle, so the x-axis divides the line in the ratio 1:2 which is the ratio AD:CD. This is another way of saying that AD is a third the length of AC, or AE is a third the length of AB.