Question:
When the origin is shifted to $(2, 3)$ by translation of axes, the coordinates of a point $P$ become $(1, -2)$. The original coordinates of $P$ are:
When the origin is shifted to $(2, 3)$ by translation of axes, the coordinates of a point $P$ become $(1, -2)$. The original coordinates of $P$ are:
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Remember the intuitive relation: $\text{Original} = \text{New} + \text{Shift}$. Simply add the coordinate values directly: $(1+2, -2+3) = (3, 1)$.
Updated On: Jun 3, 2026
- $(3, 1)$
- $(1, 5)$
- $(3, -5)$
- $(-1, 5)$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
When the origin is shifted to a new point $(h, k)$ by translation of axes, the relationship between the original coordinates $(x, y)$ and the new coordinates $(x', y')$ is given by the formulas $x = x' + h$ and $y = y' + k$.
Step 2: Meaning
Here, the shifted origin is $(h, k) = (2, 3)$ and the transformed coordinates of the point $P$ are $(x', y') = (1, -2)$. We need to determine the original coordinates $(x, y)$.
Step 3: Analysis
Using the translation formulas: \[ x = x' + h = 1 + 2 = 3 \] \[ y = y' + k = -2 + 3 = 1 \] Thus, the original coordinates of the point $P$ are $(3, 1)$.
Step 4: Conclusion
The original coordinates of the point $P$ are $(3, 1)$, which corresponds to option (A).
Final Answer: (A)
When the origin is shifted to a new point $(h, k)$ by translation of axes, the relationship between the original coordinates $(x, y)$ and the new coordinates $(x', y')$ is given by the formulas $x = x' + h$ and $y = y' + k$.
Step 2: Meaning
Here, the shifted origin is $(h, k) = (2, 3)$ and the transformed coordinates of the point $P$ are $(x', y') = (1, -2)$. We need to determine the original coordinates $(x, y)$.
Step 3: Analysis
Using the translation formulas: \[ x = x' + h = 1 + 2 = 3 \] \[ y = y' + k = -2 + 3 = 1 \] Thus, the original coordinates of the point $P$ are $(3, 1)$.
Step 4: Conclusion
The original coordinates of the point $P$ are $(3, 1)$, which corresponds to option (A).
Final Answer: (A)
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