Question

What’s the ratio of the lengths from BE to CD ?

Answer 1

From the cartesian plane shown, we can bring out two right triangles with their sides gotten from the coordinates of the points given as shown below;

From the figure above,

let BE = x

CD = y

By similarity, the corresponding ratio of the lengths of similar triangles are equal

The triangles ABE and ACD are similar, hence the ratio of their lengths will be equal

By similarity,

`\begin{gathered} (x)/(4)=(y)/(6) \\ C\text{ ross multiplying;} \\ 6x=4y \\ \text{Hence,} \\ (x)/(y)=(4)/(6) \\ (x)/(y)=(2)/(3) \\ (BE)/(CD)=(2)/(3) \end{gathered}`

Therefore, the ratio of lengths of BE to CD is 2/3.