On shifting the origin to (p, q), the coordinates of point (2, –1) changes

to (5, 2). Find p and q.

Original point = (x, y) = (2, -1)

New point = (x¹, y¹) = (5, 2)

New origin = (p, q)

∴x¹ = x - h 

⇒5 = 2 - p

∴p = -3

Similarly,

y¹ = y - k

⇒2 = -1 - q

∴q = -3

Therefore, new origin = (p, q) = (-3, -3)