Free graphing resources · Original practice
Reflect four point sets by changing the correct coordinate signs. Preserve vertex order, identify points on an axis and compare original and reflected shapes.
Reflect four point sets by changing the correct coordinate signs. Preserve vertex order, identify points on an axis and compare original and reflected shapes.
Choose Letter or A4, then download a student sheet first. Keep the separate reference or answer file closed until you have attempted the case. Every worksheet, SVG and answer is free without signup.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Original worksheet collection. Letter or A4 PDF and editable SVG.
Complete free PDF pack.
| Case | Focus |
|---|---|
| RF01 | Reflect over x-axis |
| RF02 | Reflect over y-axis |
| RF03 | Reflect over both axes |
| RF04 | Compare a point set |
All examples use original fictional data and coordinate units. They are practice material, not measured classroom results, published questions or evidence about real people.
RF01: Reflect over x-axis
| Check | Worked result |
|---|---|
| 1 | Reflection over x axis: (-4, -1), (-1, -4), (2, -1), (0, 1). |
| 2 | Points on a reflecting axis stay in place. |
| 3 | Connect corresponding points in the same order. |
The first case shows the checking pattern. Individual answer files contain the completed graph and result for every case.
Begin by examining the specific case you selected to determine which axis acts as the mirror line. For instance, case RF01 specifies a reflection over the x-axis, while RF02 targets the y-axis. Case RF03 requires reflecting over both axes simultaneously. This distinction is critical because the transformation rule depends entirely on this choice. If you are working with RF04, note that it also uses the y-axis for comparison. Identifying the correct axis prevents applying the wrong sign change to your coordinates. Always verify the axis label in the reference PDF before plotting any points to ensure your initial setup aligns with the fictional exercise requirements.
Once the axis is known, apply the specific sign change to each point in the set. For an x-axis reflection, change the sign of the y-coordinate only, turning (x,y) into (x,-y). For a y-axis reflection, change the sign of the x-coordinate only, turning (x,y) into (-x,y). When reflecting over both axes, as in case RF03, change the signs of both coordinates. Points lying directly on the reflecting axis remain unchanged. Use the supplied listed values from the student PDF to calculate these new positions accurately without relying on physical measurement or external tools.
After calculating the new coordinates, compare your results with the provided answer PDF. The listed coordinates and supplied values determine the correct answers, so your calculated points should match exactly. For example, in case RF01, the point (0,-1) remains (0,-1) because it lies on the x-axis. Check each transformed point individually to catch sign errors. Since these are original fictional practice materials, the answer key reflects the mathematical rules applied to the specific point sets. Do not expect physical printing variations to affect the listed answer key, as the solution is based strictly on the coordinate data provided in the resource pack.
| Watch for | Check instead |
|---|---|
| Changing the wrong coordinate sign for the specified axis. | Ensure you change only the y-coordinate for x-axis reflections and only the x-coordinate for y-axis reflections, keeping the other value constant. |
| Assuming points on the axis move to a different location. | Remember that points lying directly on the reflecting axis stay on that axis, so their coordinates remain unchanged during the transformation. |
| Expecting physical print alignment to match digital coordinate precision. | Rely solely on the digital coordinates and supplied values for accuracy, as physical printing tests have not been performed on these resources. |
Choose the PDF that matches your paper. Print at Actual size / 100% and turn off Fit, Shrink and browser headers. SVG is editable but an editor can rescale it; the PDF is the simpler print route. Physical printer, classroom and curriculum tests have not been completed.
The x-coordinate stays the same and y changes sign: (x,y) becomes (x,-y).
It stays in the same location because its coordinate on that axis is zero.
No. Keep the original order when connecting corresponding points.
Yes. The individual student, reference and answer files plus collection packs are free without signup. Credit Zumola under CC BY 4.0 when sharing or adapting.
Take quadrilateral ABCD with A(-4, 1), B(-1, 3), C(-1, 1) and D(-4, -2). A reflection over the y-axis changes the sign of each x-coordinate and leaves each y-coordinate unchanged. The rule is (x, y) to (-x, y). Apply it to each vertex in the same order: A' is (4, 1), B' is (1, 3), C' is (1, 1) and D' is (4, -2).
Plot the original points first, then the images, and connect A to B to C to D and back to A. The image should connect A' to B' to C' to D' and back to A'. Check that the segment between each point and its image is horizontal and that the midpoint of that segment lies on the y-axis. For A and A', the midpoint is (0, 1), which is on the axis, so the pair is consistent.
Reflection worksheets often mix tasks that look similar but need different answers. Drawing a reflected shape asks for plotted vertices and connected segments. Judging a property asks whether lengths, angles or orientation are preserved. Computing area asks for a number in square units. A composite task applies two reflections in sequence, and the order matters.
For a composite reflection, apply the first rule to every vertex, then apply the second rule to the results. Reflecting over the x-axis then the y-axis maps (x, y) to (-x, -y), which is a rotation by 180 degrees about the origin, not a single reflection. Label intermediate points clearly so the final answer can be traced back.
A reflected drawing can look plausible while containing one flipped sign. Run three quick checks. First, confirm every image point is the same distance from the mirror line as its original, on the opposite side. Second, confirm points that lie on the mirror line stay fixed. Third, confirm the vertex order is preserved so the shape is not accidentally rotated or mirrored twice.
Keep labels and margins readable: place vertex labels outside the shape where possible and leave space near the grid edge so reflected points are not crowded. If a point lands on an axis, state that it is unchanged rather than writing a new coordinate.
Reflect triangle PQR with P(2, 1), Q(5, 1) and R(2, 4) over the x-axis, then state the image coordinates and the area of the image in square units.
Over the x-axis the rule is (x, y) to (x, -y). P' is (2, -1), Q' is (5, -1) and R' is (2, -4). The original triangle has a horizontal base PQ of length 3 units and a vertical height from R to that base of 3 units, so its area is 3 times 3 divided by 2, which is 4.5 square units. Reflection preserves area, so the image also has area 4.5 square units. Check: the midpoint of P and P' is (2, 0), which lies on the x-axis.
Pick one vertex and its image, find the midpoint of the segment joining them, and confirm it lies on the mirror line. Then confirm the segment is perpendicular to that line.
A single reflection flips a shape across a line and reverses orientation. A rotation turns the shape about a point and preserves orientation. Two reflections can produce a rotation, so label intermediate steps.
No. A reflection preserves lengths and angles, so the area in square units stays the same. If your computed areas differ, check for a plotting or counting error.
