Question

Triangle ABC is similar to triangle ADE, which is formed with angle A and side AD, as shown.


What could be the coordinates of point E?

(2,–1)
(–1,2)
(–3,–1)
(–1,–3)

Answer 1

I don't have the diagram, coordinates, or locations of A, B, C, D, so I can't decide which of the four choices is correct. Could you either upload the figure or give the coordinates of A, B, C and D (or describe which sides/points correspond in the similarity)?

If you prefer to solve it yourself, here's the method to use once you have A, B, C and D:

1. Decide which sides correspond. If triangle ABC is similar to triangle ADE with the common angle at A, usually AB corresponds to AD and AC corresponds to AE. (Confirm from the diagram.)

2. Compute the similarity scale factor k = |AD| / |AB|.

3. Then AE = k · AC as vectors. So the coordinates of E are
E = A + k (C − A).

4. Alternatively, if AB corresponds to AE and AC corresponds to AD, use k = |AD| / |AC| and E = A + k (B − A).

5. To check a candidate E, verify both:
- AE / AC (length ratio) equals AD / AB (the scale factor), and
- the angle at A is preserved (the directions of AE and AC have the same angle as AD and AB).

Send the missing coordinates or the picture and I’ll compute which of the four choices is correct.