Point C (4, -1) is reflected in the line x = 6 to point D. Work out the coordinates of D.
How to approach this question
1. Identify the coordinates of point C: (4, -1).
2. Identify the line of reflection: x = 6. This is a vertical line passing through 6 on the x-axis.
3. When reflecting in a vertical line, the y-coordinate stays the same. So, the y-coordinate of D is -1.
4. Find the horizontal distance from point C to the line of reflection. The x-coordinate of C is 4, and the line is at x = 6. The distance is 6 - 4 = 2 units.
5. The reflected point D will be the same distance on the other side of the line. So, move 2 units to the right from the line x = 6.
6. The new x-coordinate will be 6 + 2 = 8.
7. Combine the new x-coordinate and the unchanged y-coordinate to get the coordinates of D.
Full Answer
Reflection is a transformation that flips a shape or point across a line.
1. **The point to reflect:** C is at (4, -1).
2. **The line of reflection:** x = 6. This is a vertical line where every point on it has an x-coordinate of 6.
3. **Reflecting in a vertical line:**
- The y-coordinate of the reflected point will be the same as the original point. So, the y-coordinate of D is -1.
- The horizontal distance from the original point to the line of reflection is the same as the horizontal distance from the line to the reflected point.
4. **Calculate the new x-coordinate:**
- The horizontal distance from C (x=4) to the line (x=6) is 6 - 4 = 2 units.
- Point D must be 2 units to the *other side* (the right side) of the line x = 6.
- The x-coordinate of D is 6 + 2 = 8.
5. **The coordinates of D:** Combining the x and y coordinates, D is at (8, -1).
Common mistakes
✗ Changing the y-coordinate.
✗ Calculating the distance to the y-axis instead of the line x=6.
✗ Adding the distance incorrectly (e.g., 4+2=6 instead of 6+2=8).
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