Translation Math exercise - Free Printable

Let’s solve each part step by step.

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Problem 1: Identify the correct translation.

We are given four triangles labeled A, P, Q, and R on a coordinate grid. We need to find which one is a translation of triangle A.

A translation means moving a shape without rotating or flipping it — just sliding it up/down/left/right. The size and orientation must stay exactly the same.

Look at triangle A:
- Its bottom-left corner is at (1,6)
- It goes right to (4,6) → base = 3 units
- It goes up to (1,9) → height = 3 units
→ So it’s a right triangle with legs of 3 units, pointing up-right.

Now check others:

- Triangle P: Same size? Let’s see — from (6,6) to (10,6) → base = 4 units. Too big! Not same size → not a translation.
Wait — actually, let me double-check coordinates.

Actually, looking again:

Triangle A:
- Bottom-left: (1,6)
- Bottom-right: (4,6) → width = 3
- Top-left: (1,9) → height = 3

Triangle P:
- Bottom-left: (6,6)
- Bottom-right: (10,6) → width = 4 → different size → NOT translation.

Triangle Q:
- Bottom-left: (6,3)
- Bottom-right: (8,3) → width = 2
- Top-left: (6,5) → height = 2 → smaller → NOT translation.

Triangle R:
- Bottom-left: (1,1)
- Bottom-right: (4,1) → width = 3
- Top-left: (1,4) → height = 3 → SAME SIZE AND SHAPE as A!
And it’s oriented the same way — right angle at bottom-left, hypotenuse going up-right.

So triangle R is just triangle A moved down 5 units (from y=6 to y=1). No rotation, no flip → this IS a translation.

✔ So answer for Problem 1 is R

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Problem 2: Calculate the translations.

Part a: Rectangle A to A’

Rectangle A:
- Left side at x=1, right side at x=4 → width = 3
- Bottom at y=5, top at y=9 → height = 4

Rectangle A’:
- Left side at x=7, right side at x=10 → width = 3 → same
- Bottom at y=5, top at y=9 → same height

So only horizontal movement.

From x=1 to x=7 → that’s +6 squares to the right.

Vertical position didn’t change (y stays 5 to 9).

So translation is 6 squares to the right.

Part b: Diamond P to P’

Diamond P:
- Center seems to be around (5,8) — but let’s pick a point to track.

Top point of P: (5,9)
Bottom point of P: (5,7)

Diamond P’:
Top point: (5,3)
Bottom point: (5,1)

So top point moved from y=9 to y=3 → that’s down 6 squares.

Left/right didn’t change — still centered at x=5.

So translation is 6 squares down.

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Final Answer:

1. R
2a. 6 squares to the right
2b. 6 squares down