Coordinate geometry
Use coordinates to compare distances, midpoints and moving points. Test relationships on a grid.
Midpoints and distances
1 comparison · No time limit · Explore after checking
Example
Example
Compare the two quantities using the givens.
Review the comparison
P = (−3, t), Q = (5, −t), −3 ≤ t ≤ 3.
M is the midpoint of segment PQ.
Both axes use equal units. Use the stated coordinates and constraints.
x-coordinate of M
0
Choose an answer to try the example.
Why?
Explore the relationship
Make segment PQ horizontal.
In this drawing
Need a clue?
A horizontal segment has equal endpoint heights. Here they are t and −t.
Example positions
Move the endpoints to opposite heights. Track their midpoint.
The controls preserve the givens. Examples illustrate the rule; the explanation proves it.
Go further Apply the idea
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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
Use coordinate differencesUse coordinates to compare distances, midpoints and moving points. Test relationships on a grid.
For a broader mix of practices, explore the geometry practice test. Membership is required to start a test.
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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 used