A translation is when a shape is moved up, down, right, or left without being flipped or rotated. The size of the shape remains the same after translation. To translate a shape, each point on the shape must move the same distance.
Translation on the graph example:
Let us see how to solve a shape on the coordinate grid.
Transformation:
a) Shape A has been transformed to shape B by translating it 6 units right and 7 units down.
b) You can notice from the above transformation that after translation, the new shape looks precisely similar to the original shape.
The questions on translation can be of two types:
Apply some transformation on some shapes on the grid. In which you will pick the vertices of the shape, and move each of the vertices as asked.
Some translation has been done already and you will be asked to write down what translation has been applied. You will pick any of the vertices and first look for how much the figure has been moved on the x-axis (left or right), then on the y-axis (up or down). Those numbers will be your translation (make sure the signs are correct)
You will get a more clear idea as we go through the following examples.
Solved Examples:
Example 1:
A slider takes you from one point on the grid to another point. The first number in a slider refers to left or right, and the second number to up or down.
For example, the slider [4, -5] takes you from P to R, because from P you move 4 units to the right and 5 units down to get to B.
Likewise, from R to Q, the slider is [1, 5] because from R you would go 1 unit to the right and 5 units up.
a. What slider takes you from S to Q?
b. Slider [-3, -7] takes you from Q to T. Mark point T on the diagram above.
Solution:
a. To reach Q from S, you would need to move 3 units to the right and 5 units up. So the slider would be [3, 5].
b. To reach T from Q, we will first move 3 units to the left and 7 units down as shown in the diagram below:
Example 2:
Shape A has been plotted on the centimetre grid below. Translate shape A as 5 squares right and 4 squares up. Label your shape B.
Solution:
Squares here referred to the squares on the grid, so simply take all the vertices one by one and draw them on the grid and you will have your shape B.
Example 3:
Translate shape P 6 units down and 7 units left. Label the new shape Q.
Solution:
As asked in the question, we will draw shape Q by translating each vertex of the shape P 6 units down and 7 units left, as shown below:
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