Reflect Across Y Axis Calculator

Reflect points, lines, shapes, and tables with steps. Compare x signs before plotting mirrored results. Export neat files for class, study, and quick review.

Calculator

Example Data Table

Input Rule Output Note
(4, 3) (x, y) → (-x, y) (-4, 3) Right side moves left.
(-7, 2) (x, y) → (-x, y) (7, 2) Left side moves right.
(0, -5) (x, y) → (-x, y) (0, -5) Point stays on y axis.
2x + 3y - 6 = 0 A becomes -A -2x + 3y - 6 = 0 Line is mirrored.

Formula Used

The y axis reflection formula is:

(x, y) → (-x, y)

The x coordinate changes sign. The y coordinate stays unchanged.

For a line written as Ax + By + C = 0, the reflected line is:

-Ax + By + C = 0

For polygons, reflect each vertex. Area and perimeter remain equal.

How to Use This Calculator

  1. Select single point, batch points, polygon, or line mode.
  2. Enter the required coordinates or equation values.
  3. Choose decimal places for the final answer.
  4. Press Calculate to view the mirrored result.
  5. Use CSV or PDF buttons to download your report.

Reflection Across the Y Axis

A y axis reflection is a horizontal flip. Every point moves to the opposite side of the vertical axis. The height stays unchanged. The distance from the axis also stays unchanged. This makes the rule simple, but it is still useful in geometry, design, mapping, and coordinate checks.

What the Calculator Does

This calculator handles single points, many points, polygon vertices, and line equations. It changes each x value to its opposite sign. It keeps each y value the same. It also shows the ordered pair rule, distance from the y axis, and quadrant changes. When polygon mode is used, it keeps area and perimeter for comparison.

Why the Rule Works

The y axis is the mirror line. Any point on this line has an x value of zero. A point to the right has a positive x value. A point to the left has a negative x value. Reflection swaps these positions. The point does not move up or down. Only the horizontal direction changes.

Working With Shapes

A shape can be reflected by transforming every vertex. Join the new vertices in the same order. The reflected shape has the same size. Its orientation is reversed. This is useful when checking symmetry or preparing mirrored parts. Designers can use it before drawing a second half of a plan.

Line Equation Support

The calculator can also reflect a line written as Ax + By + C = 0. Under a y axis reflection, x is replaced by -x. This changes A to -A. B and C remain the same. The resulting equation describes the mirror image of the original line.

Practical Uses

Students can verify homework steps quickly. Teachers can create examples with exported reports. Engineers can mirror simple coordinate layouts. Builders can check symmetrical drawings. The CSV file helps with spreadsheets. The PDF file helps with sharing a clean result sheet.

Accuracy Tips

Use decimal precision that matches your task. Enter points in clear pairs. Keep polygon vertices in order. Avoid mixing commas and spaces in confusing ways. Review the table before exporting. Use notes for repeated checks. A reflected point should always have the same y value. Its x value should always have the opposite sign.

FAQs

1. What does reflecting across the y axis mean?

It means the point is mirrored across the vertical axis. The x value changes sign. The y value stays the same.

2. What is the main formula?

The formula is (x, y) → (-x, y). It works for every point on a coordinate plane.

3. Does the y coordinate ever change?

No. A y axis reflection only changes the horizontal position. The vertical position remains unchanged.

4. What happens to a point on the y axis?

A point on the y axis has x = 0. Its reflection is the same point, because -0 is still 0.

5. Can I reflect a polygon?

Yes. Reflect every vertex using the same rule. Then connect the new vertices in the same order.

6. Does polygon area change after reflection?

No. Reflection keeps the same size. Area and perimeter stay equal, but orientation is reversed.

7. How is a line equation reflected?

For Ax + By + C = 0, change A to -A. The reflected equation becomes -Ax + By + C = 0.

8. Why use CSV and PDF downloads?

CSV is useful for spreadsheets. PDF is useful for printing, sharing, and attaching a clean result to class work.

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