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

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.

ago by Top Rated User (781k points)

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