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Position and Direction - Translation of shapes

Grade 4IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Translation means moving a shape or a point from one position to another by sliding it.

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During translation, the shape does not rotate, flip, or change its size; it only changes its location.

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A translation is described by how many units a shape moves horizontally (left or right) and vertically (up or down).

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To translate a whole shape, move every vertex (corner) the same distance and in the same direction, then join them back together.

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The original shape and the translated shape are 'congruent', meaning they are exactly the same size and shape.

📐Formulae

New x-coordinate=Original x+Units moved Right\text{New } x\text{-coordinate} = \text{Original } x + \text{Units moved Right} (or −Units moved Left- \text{Units moved Left})

New y-coordinate=Original y+Units moved Up\text{New } y\text{-coordinate} = \text{Original } y + \text{Units moved Up} (or −Units moved Down- \text{Units moved Down})

Translation Vector (Introductory)=(horizontal changevertical change)\text{Translation Vector (Introductory)} = \binom{\text{horizontal change}}{\text{vertical change}}

💡Examples

Problem 1:

Point AA is located at (2,5)(2, 5) on a coordinate grid. If Point AA is translated 33 units to the right and 44 units down, what are the new coordinates of Point A′A'?

Solution:

(5,1)(5, 1)

Explanation:

Start at the xx-coordinate 22 and add 33 (2+3=52 + 3 = 5). Start at the yy-coordinate 55 and subtract 44 because the movement is down (5−4=15 - 4 = 1). The new position is (5,1)(5, 1).

Problem 2:

A square has a vertex at (1,1)(1, 1). The square is translated so that this vertex moves to (4,1)(4, 1). Describe the translation.

Solution:

3 units to the right.

Explanation:

The xx-coordinate changed from 11 to 44 (4−1=34 - 1 = 3), which is a movement of 33 units to the right. The yy-coordinate remained 11, meaning there was no vertical movement (0 units up/down).

Problem 3:

A triangle has vertices at P(1,2)P(1, 2), Q(3,2)Q(3, 2), and R(2,4)R(2, 4). If the triangle is translated 22 units left and 33 units up, what are the new coordinates for vertex QQ?

Solution:

Q′(1,5)Q'(1, 5)

Explanation:

To find the new position of vertex Q(3,2)Q(3, 2), subtract 22 from the xx-coordinate (3−2=13 - 2 = 1) and add 33 to the yy-coordinate (2+3=52 + 3 = 5). The new vertex Q′Q' is at (1,5)(1, 5).