complex numbers, similar triangles and all that stuff (1 Viewer)

[sasquatch]

Im having trouble trying to represent a point to make two triangles similar...

The questions asks:

If A, P, Q respectively represent the Argand diagram complex numbers 1, z_1, z_2, construct R so that the triangles OAP and ORQ are similar. Find the complex number representing point R.

What im having trouble with is plotting the points. After placing z_1 and z_2 in random spots, im then confused to where i should place R to ensure the triangles are similar.

 

[Riviet]

Consider parallel lines and equal corresponding angles to help you draw the two triangles. Try drawing this example. Mark A(1,0) with a dot then mark where (1/2,1/2) would be as P with a dot and draw that triangle. Now label origin as O, Q at (1/2,-1/2). Now extend OP diagonally down to the left and draw RQ such that RQ || OA and there you have your similar triangles.

 

[sasquatch]

but with this way, um can the ratio of OA....man im confused..

 

[Riviet]

Man, i really need to show you on an attachment, except i don't know how to scan stuff let alone upload them on BoS.