Question

In the figure if P (36, 48), then find the coordinates of A, B, M

Answer 1

∆ OMP is a right triangle

\(\therefore \,OP=\sqrt{48^2+36^2}=60\)

∆ PAO, ∆ OMP are similar

= \(\frac{OA}{OP}=\frac{OP}{PM}\) 

\(\therefore\,OA=\frac{OP^2}{PM}=\frac{60^2}{48}=75\)

∆ OMP, ∆ OPB are similar.

= \(\frac{OB}{OP}=\frac{OP}{OM}\)

\(\therefore \,OB=\frac{OP^2}{OM}=\frac{60^2}{36}=100\)

Coordinates of M (36, 0)

Coordinates of A (0, 75)

Coordinates of B (100, 0)