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,
[tex]\begin{gathered} \frac{x}{4}=\frac{y}{6} \\ C\text{ ross multiplying;} \\ 6x=4y \\ \text{Hence,} \\ \frac{x}{y}=\frac{4}{6} \\ \frac{x}{y}=\frac{2}{3} \\ \frac{BE}{CD}=\frac{2}{3} \end{gathered}[/tex]
Therefore, the ratio of lengths of BE to CD is 2/3.
