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Mentally find the coordinates of the image of under each transformation.
For each point , find its image under the transformation .
Here are some transformation rules. Apply each rule to quadrilateral , and graph the resulting image. Then describe the transformation.
Square has been translated by the directed line segment from to . The result is square .
Two squares on coordinate plane, origin O. Horizontal x axis from negative 2 to 6. Vertical axis from negative 4 to 4. Square A B C D with vertices A at negative 1 comma 1, B at 1 comma 1, C at 1 comma negative 1 and D at negative 1 comma negative 1. Point Q at negative point 5 comma 1. Square A prime B prime C prime D prime with vertices A prime at 4 comma 0, B prime at 6 comma 0, C prime at 6 comma negative 2, D prime at 4 comma negative 2, and Q prime at 4 point 5 comma 0.
Here is a list of coordinates in the original figure and corresponding coordinates in the image. Do you see the rule for taking points in the original figure to points in the image?
| original figure | image |
|---|---|
This table looks like a table that shows corresponding inputs and outputs of a function. A transformation is a special type of function that takes points in the plane as inputs and gives other points as outputs. In this case, the function’s rule is to add 5 to the -coordinate and subtract 1 from the -coordinate.
We write the rule this way: .