Question

Given triangle ABC with AB = 3 , BC = 5 , and CA = 6. X is the midpoint of AC and Y is the midpoint of CB. What is the relationship between XY and AB?

Answer 1

From the calculations, XY is parallel to AB and the length of AB is twice that of XY

Explanation:

Here, we want to find the relationship between XY and AB

we start by drawing an image representing the information in the question

Please check the attachment for this;

Firstly, from the image drawn, the side XY is parallel to AB and we have a set of similar triangles

These are triangles ABC and CXY

If two triangles are similar, then, the ratio of their sides are equal

Thus, mathematically;

AC/AB = CX/XY

6/3 = 3/XY

XY = (3 * 3)/6

XY = 9/6

XY = 1.5