find the two points on AB that divide a segment into congruent parts point A has (0,0) and point B coordinates (9,6) explain your method

Question

find the two pints AB that divide the segment into three congruent parts. point A has coordinates (0,0) and point B has coordinates (9,6). explain your method

Answer 1

(x - 0)/(9 - 0) = 1/3 and (y - 0)/(6 -0) = 1/3

x = 3; y = 2

(3, 2) is the point that is one - third of the way from the origin.

(x - 0)/(9 - 0) = 2/3 and (y - 0)/(6 - 0) = 2/3

x = 6 and y = 4

(6, 4) is the point that is two - thirds of the way from the origin.

Look at it like this, you know that the point P you're interested in has an (x, y) coordinate that is one - third (or two - third) of the way from the origin. So, AP/AB = 1/3 (or AP/AB = 2/3 depending on which point you're focusing on at the time). In either case, all you're saying is that the distance of the x's of AP is 1/3 the distance of the x's of AB. And, the distance of the y's for AP is 1/3 the distance of the y's for AB.

Hope that makes some sense.

Mr. K