How coordinates of **P'** are (y, x)?

Question

I'm learning Trigonometry right now and at current about trigonometry functions. I'm quite confused right now in a section of the chapter. Please have a look at the image below.
How triangle OMP and OM'P' are congruent? Both triangles are 90° but how sides of both the triangle are equal?

Also how the coordinates of $P'$ are $(y, x)$.
Sorry if I'm asking foolish questions. I have just started learning mathematics with my own. Please help. Thankyou in advance.

Answer 1

OPM+POM=90° (Sum of angles of triangle=180° and PMO=90°)

So, OPM= 90°-POM=90°-theta=P'OM' (i)

Similarly, OP'M'=POM (ii)

OP=P'O (Given) (iii)

Therefore OPM is congruent to P'OM'