Question

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 'O₁ X₁ and suppose O₁ has coordinates (9,5) with respect to X 'OX ↔ Y 'OY. What are the coordinates of P in the system X₁'O₁ X₁↔ Y₁'O₁ Y₁?

Answer 1

Solution:

The two coordinate system one having X'OX and Y'OY as lines of axis and another Coordinate system parallel to original  coordinate system is  X₁ 'O₁X₁ and Y₁ 'O₁Y₁.

The Original coordinate system have Center O at (0,0) has been translated  to  new coordinate system having Center O₁ , the coordinates being (9,5).

Point P in the Original coordinate system has coordinates (-8,3).

To find the Coordinates of P in new system ,we have to use following formula

$X= X_{1} + p, Y= Y_{1} + q$ where (p,q)= (9,5)

$X=X_{1}+p\\\\-8 =X_{1} + 9 \\\\ X_{1}= -8-9 \\\\ X_{1}= -17 \\\\Y=Y_{1}+q\\\\ 3 = Y_{1} +5 \\\\ Y_{1}= 3 -5 \\\\ Y_{1}=-2$

So, the coordinate of P in the System  X₁'O₁ X₁↔ Y₁'O₁ Y₁ is  (-17, -2)