MathDB

max value of the y -coordinate of P(x,y) after triangle rotation

Source: 2015 Argentina OMA L3 p3

June 19, 2020

geometryanalytic geometryrotationcoordinate geometrygeometric transformation

Problem Statement

Consider the points

O = (0,0), A = (- 2,0)

and

B = (0,2)

in the coordinate plane. Let

E

and

F

be the midpoints of

OA

and

OB

respectively. We rotate the triangle

OEF

with a center in

O

clockwise until we obtain the triangle

OE'F'

and, for each rotated position, let

P = (x, y)

be the intersection of the lines

AE'

and

BF'

. Find the maximum possible value of the

y

-coordinate of

P