If the origin gets shifted to (2, 2), then what will be the new coordinates of the point (4, -2)?
(a)(- 2, 4)
(b)(2, 4)
(c)(4, 2)
(d)(2, - 4)

Options

A. (- 2, 4)
B. (2, 4)
C. (4, 2)
D. (2, - 4)

Answer

To find the new coordinates of the point (4, -2) after shifting the origin to (2, 2), we can follow these steps:

### Step 1: Understand the Shift of Origin
When the origin shifts from (0, 0) to (2, 2), we need to adjust the coordinates of any point accordingly. The new coordinates will be calculated by subtracting the new origin's coordinates from the original point's coordinates.

### Step 2: Set Up the Equation
Let the original point be represented as (x', y') = (4, -2). The new origin is (2, 2). We can express the new coordinates (x, y) as:
- x = x' - 2
- y = y' - 2

### Step 3: Substitute the Original Coordinates
Now, substitute the original coordinates into the equations:
- For x:
\[ x = 4 - 2 \]
- For y:
\[ y = -2 - 2 \]

### Step 4: Calculate the New Coordinates
Now, perform the calculations:
- For x:
\[ x = 4 - 2 = 2 \]
- For y:
\[ y = -2 - 2 = -4 \]

### Step 5: Write the New Coordinates
Thus, the new coordinates of the point (4, -2) after shifting the origin to (2, 2) are:
\[ (2, -4) \]

### Conclusion
The correct answer is option (d) (2, -4).

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