Calculator
Example Data Table
| Original Point | Y-Axis Reflection | Explanation |
|---|---|---|
| (5, 2) | (-5, 2) | The x-value changes sign. The y-value stays same. |
| (-3, 7) | (3, 7) | The point moves to the opposite side of the y-axis. |
| (0, -4) | (0, -4) | A point on the y-axis does not move. |
| (8, -6) | (-8, -6) | Only horizontal position changes after reflection. |
Formula Used
A reflection across the y-axis changes the sign of the x-coordinate. The y-coordinate remains unchanged.
Main formula: (x, y) → (-x, y)
Matrix form: [[-1, 0], [0, 1]] × [x, y] = [-x, y]
The distance from the original point to the y-axis is |x|.
The total horizontal movement from the original point to the reflected point is 2|x|.
How to Use This Calculator
Enter one coordinate pair per line in the input box. Choose the decimal precision you want. Add a label prefix if you are reflecting several points. Select extra options if you want distance, movement, or rule details. Press the calculate button. The reflected points appear above the form and below the header. Use the CSV or PDF buttons to save your results.
Understanding Y-Axis Reflection
What the Reflection Means
A y-axis reflection creates a mirror image across the vertical axis. The point moves horizontally, but it keeps the same height. This makes the rule simple and useful. Every x-value changes to its opposite. Every y-value remains unchanged. So the point (6, 4) becomes (-6, 4). The point (-9, 2) becomes (9, 2). A point already on the y-axis stays fixed.
Why the Rule Works
The y-axis is the line where x equals zero. It divides the coordinate plane into left and right sides. Reflection means equal distance on the opposite side. A point with x equal to 5 is five units right. Its reflection must be five units left. That gives x equal to -5. The vertical position is not changed. This is why y remains the same.
Using Multiple Points
This calculator supports many points at once. That helps when reflecting shapes, graphs, or tables. Enter each point on a new line. The tool returns a clean table. You can compare original and reflected coordinates quickly. This is helpful for assignments and graph checks. It also reduces sign mistakes. The export buttons make records easy to share.
Graphing Tip
Plot the original point first. Then count the same horizontal distance across the y-axis. Keep the same vertical level. Mark the new point. Repeat this for every coordinate. Connect the reflected points in the same order. The final image should look like a horizontal mirror. Check points with x equal to zero. They should stay exactly where they started.
FAQs
1. What is a y-axis reflection?
A y-axis reflection flips a point or shape across the vertical axis. The reflected image appears the same distance from the y-axis on the opposite side.
2. What is the rule for reflection over the y-axis?
The rule is (x, y) → (-x, y). Change the sign of x. Keep the y-value unchanged.
3. Does the y-coordinate ever change?
No. In a y-axis reflection, the y-coordinate stays the same. Only the x-coordinate changes sign.
4. What happens to a point on the y-axis?
A point on the y-axis has x equal to zero. Its reflection is the same point because zero changes to zero.
5. Can I reflect multiple points at once?
Yes. Enter one point on each line. The calculator will reflect every valid coordinate pair and display them in a table.
6. What format should I use for coordinates?
You can use formats like 4, 3 or (4, 3). You can also separate x and y values with a space.
7. How is distance from the y-axis found?
The distance from a point to the y-axis is the absolute value of x. For example, x = -6 gives distance 6.
8. Can I export the reflected points?
Yes. After calculating, use the CSV or PDF button to download the result table for later use.