Reflection and Translation on a Grid
Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed
What a learner can do afterwards
- Reflect a triangle in a vertical mirror line on a coordinate grid and state the new coordinates
- Translate a shape 3 units right and 2 units up and describe the movement
- Explain that a reflected/translated shape is congruent to the original
1 · Read
You already know how to flip a shape over a line and how to slide it across a grid. Now you will do both of these on a coordinate grid, and describe the shape's new position using coordinates.
Triangle ABC has corners at (2, 1), (5, 1), and (3, 4). Reflect it in the vertical line x = 0. Each y-coordinate stays the same, but each x-coordinate flips sign: A' (-2, 1), B' (-5, 1), C' (-3, 4).
A square's corner starts at (1, 2). It slides 3 units right and 2 units up. Add 3 to the x-coordinate and 2 to the y-coordinate: (1 + 3, 2 + 2) = (4, 4).
After a reflection or a translation, the shape is congruent to the original. Congruent means exactly the same size, with the same angles, just sitting in a new spot on the grid.
Reflecting or translating a shape only changes its position on the grid. The shape itself, its size and its angles, never change.
More to read
Symmetry review
Reflection flips a shape across a mirror line. On squared paper with a vertical mirror, each corner jumps to the same distance on the other side. A vertex 1 square right of the line lands 1 square left. Only one coordinate changes in a vertical mirror. The x-coordinate jumps across, the y-coordinate stays put. Track x and the reflection lands correctly every time.
How would you describe these figures?
Translation slides a shape without turning it. A move of 3 right and 2 up adds 3 to every x and 2 to every y. Order never matters: 3 right then 2 up lands where 2 up then 3 right lands. Describe moves fully or partners get lost. Say both the sideways and the up-down amounts with their directions. Two translations in a row simply add: 2 right then 3 right is 5 right.
Quadrilaterals review
Reflected and translated shapes stay congruent. Sides keep their lengths and corners keep their angles, so the image stacks exactly onto the original. No reflection ever stretches a side. Use congruence to catch mistakes. If an image side looks longer, the points went wrong. Measure one side before and after any move to prove nothing changed.
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2 · Watch
به انگلیسیTake it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.