Move a shape without resizing it

1 · Learn

A translation slides each point equally. A reflection gives a mirror image, placing corresponding points the same perpendicular distance from the mirror line on opposite sides.

Both preserve side lengths and angle sizes. A reflection can reverse orientation; a translation does not turn or flip the shape. Use coordinates to check every vertex.

In the diagram the solid triangle has corners (1,1), (3,1), (1,3). Its dashed mirror image across x = 4 has corners (7,1), (5,1), (7,3). Match each pair: their horizontal distances from the mirror line are equal. Both triangles have the same side lengths.

2 · Worked example

The example point reaches the same place under two different transformations, but other points may not. One point alone may not identify how a whole shape moved.

3 · Your turn

Reflect (3,2) across the vertical line x = 5. Then translate the original point two units up. Give both results.

4 · Apply your learning

Draw a triangle in the first quadrant and show a reflection in a vertical line and a translation separately. Check corresponding vertices.