Coordinate Geometry and Review flashcards

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How do you read the center and radius from (x − h)² + (y − k)² = r²?Equations of Circles: The center is (h, k) and the radius is r. Watch the signs: x − 3 means h = 3, x + 3 means h = −3.
What is the standard form of the equation of a circle?Equations of Circles: (x − h)² + (y − k)² = r², where (h, k) is the center and r² is the radius squared.
How do you test whether a point lies on a circle?Equations of Circles: Put a point’s coordinates into the equation. If both sides match, it lies on the circle.
How do you use slopes in a coordinate proof?Coordinate Proofs: Find slopes of two different lines. Equal slopes mean parallel; negative reciprocals mean perpendicular.
How do you use distance in a coordinate proof?Coordinate Proofs: Use the distance formula, which comes from a right triangle whose legs are the coordinate changes; the hypotenuse is the distance. Equal distances show congruent segments.
How do you use midpoints in a coordinate proof?Coordinate Proofs: Average two x-values and two y-values. If diagonals share a midpoint, they bisect each other.
What does a translation do to every point?Transformations on the Coordinate Plane: It moves every point the same horizontal and vertical distance: (x, y) → (x + a, y + b).
What are the coordinate rules for reflecting over the x-axis and y-axis?Transformations on the Coordinate Plane: x-axis: (x, y) → (x, −y). y-axis: (x, y) → (−x, y).
What is the rule for a 90° counterclockwise rotation about the origin?Transformations on the Coordinate Plane: (x, y) → (−y, x).
How do you choose a method for a multi-topic geometry problem?Modeling and Cumulative Problems: Look at the givens before choosing a tool: right angle suggests Pythagoras, matching shapes suggest similarity.
How should you approach a multi-step geometry problem?Modeling and Cumulative Problems: Some problems need more than one step. Write what each step finds before moving to the next.
How do you check a geometry answer?Modeling and Cumulative Problems: Put the answer back into the original question, and make sure the units and diagram conditions make sense.