Transformations
Translate, reflect, rotate and scale figures. Explore what changes and what stays the same.
Translations and reflections
1 comparison · No time limit · Explore after checking
Example
Example
Compare the two quantities using the givens.
Review the comparison
P = (−2, −1), Q = (1, 2).
Translate both points by (t, 1) to obtain P′ and Q′.
−2 ≤ t ≤ 2.
Both axes use equal units. Use the stated coordinates and constraints.
P′Q′²
17
Choose an answer to try the example.
Why?
Explore the relationship
Place P′ on the y-axis.
In this drawing
Need a clue?
A point on the y-axis has x = 0. Start from xP = −2.
Example positions
Slide the translated segment. Observe which coordinate differences stay fixed.
The controls preserve the givens. Examples illustrate the rule; the explanation proves it.
Go further Apply the idea
Further practice does not change your comparison score.
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Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Choose whether Quantity A is greater, Quantity B is greater, the quantities are equal, or the relationship cannot be determined. Use only the stated givens. A drawing shows one possible case.
Your first checked answer counts. A shown answer counts as 0 correct. A checked comparison is saved immediately, so you can explore afterward without losing your result. An unfinished comparison is not saved as a result.
After checking, use the controls to solve an exploration goal. When the relationship cannot be determined, save two valid cases with different comparisons. Open Go further to apply the idea to a new question. These activities are optional and do not change your score.
Angles and trigonometric functions use degrees. Levels increase the mathematical complexity; they do not measure IQ.
About this practice
Learn a method
Track a transformationTranslate, reflect, rotate and scale figures. Explore what changes and what stays the same.
For a broader mix of practices, explore the geometry practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used