A point P has coordinates (7,10) in a coordinate system X′OX ↔ Y′OY. Suppose it has coordinates (10,7) in another coordinate system X′₁O₁X₁↔ Y′₁O₁Y₁ with X′OX || X′₁O₁X₁. Find the coordinates of O₁ in the system X′OX ↔ Y′OY.

(If a point P has coordinates (x1,y1) in a coordinate system X ′OX ↔ Y′OY, and if O has coordinates (a,b) in another system X₁′O₁X₁↔ Y₁′O₁Y₁ with X ′OX || X ′O₁X₁, then the coordinates of P(say x,y) in the new system X₁′O₁X₁↔ Y₁′O₁Y₁ will be x = x1 + a and y = y1 + a)

Here, x = 7, y = 10, x1 = 10, and y1 = 7

⇒ a = x - x1

⇒ a = 7 - 10

⇒ a = -3

And, b = y - y1

⇒ b = 10 -7

⇒ b = 3

⇒ the coordinates of O₁ in the system X′OX ↔ Y′OY are (-3, 3).