Suppose P is a point with coordinates (−8,3) with respect to a coordinate system X’OX ↔ Y’OY. Let X₁’O₁X₁↔ Y₁’O₁Y₁ be another system with X’OX ║X₁’O₁X₁ and suppose O₁ has coordinates (9,5) with respect to X ’OX ↔ Y ’OY. What are the coordinates of P in the system X₁’O₁X₁↔ Y₁ ’O₁Y₁?

In the figure, we have two points marked, P = (-8, 3) and O₁ = (9, 5)

According to question O₁ is the origin for a different coordinate system, X₁’O₁X₁↔ Y₁’O₁Y₁.

For coordinates of P in the new system, we have to find the distance between O₁and point P, measured FROM P.

By measuring distance on the graph above, we get

X₁= -17 and Y₁= -2

⇒ So, the coordinates of Point P in new system is (-17, -2)

OR,

Given, x= -8, y= 3

and a= 9, b=5 (Coordinates of O₁)

As we know, x= a + x’

-8 = 9+ x’

x’ = -8-9

x’ = -17

similarly,

y= b + y₁

3 = 5+ y₁

y₁ = 3-5

y₁ = -2

New coordinate, (x₁, y₁) are (-17,-2)