CMClearMathAcademy

Coordinate Geometry and Transformations Checkpoint

A free Geometry lesson from the “Coordinate Geometry and Proof” unit, with a worked example and practice problems including step-by-step solutions.

This checkpoint reviews transformations, dilations, distance, midpoint, circle equations, and slope evidence. Students need to connect diagrams, coordinates, and algebraic evidence in one mixed set. In Coordinate Geometry and Proof, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.

What you'll learn

Why it matters: Geometry assessments mix diagram reading, formulas, coordinates, proof logic, and context so students practice choosing evidence rather than memorizing a single cue.

Worked example

Problem. Worked example from Transformations on the Coordinate Plane: Translate (2, 5) right 3 and down 4.

  1. Warm-up: First identify exactly what the question is asking: Translate (2, 5) right 3 and down 4.
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Add 3 to x and subtract 4 from y.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: (5, 1)

Practice problems

1. Coordinate Geometry and Transformations Checkpoint review case A from Transformations on the Coordinate Plane: Translate (2, 5) right 3 and down 4.

Choices: (5, 1) · (-1, 9) · (5, 9) · (-1, 1)

Show solution
  1. Warm-up: First identify exactly what the question is asking: Translate (2, 5) right 3 and down 4.
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Add 3 to x and subtract 4 from y.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: (5, 1)

2. Coordinate Geometry and Transformations Checkpoint review case B from Transformations on the Coordinate Plane: Reflect (-3, 8) across the x-axis.

Choices: (-3, -8) · (3, 8) · (3, -8) · (-8, -3)

Show solution
  1. Warm-up: First identify exactly what the question is asking: Reflect (-3, 8) across the x-axis.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Keep x, change y's sign.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: (-3, -8)

3. Coordinate Geometry and Transformations Checkpoint review case C from Transformations on the Coordinate Plane: Reflect (-6, -2) across the y-axis.

Choices: (6, -2) · (-6, 2) · (6, 2) · (-2, -6)

Show solution
  1. Core Practice: First identify exactly what the question is asking: Reflect (-6, -2) across the y-axis.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Change x's sign, keep y.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: (6, -2)

4. Coordinate Geometry and Transformations Checkpoint review case D from Transformations on the Coordinate Plane: Rotate (4, 1) 180 degrees about the origin.

Choices: (-4, -1) · (-1, 4) · (1, -4) · (4, -1)

Show solution
  1. Core Practice: First identify exactly what the question is asking: Rotate (4, 1) 180 degrees about the origin.
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. A 180-degree rotation changes both signs.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: (-4, -1)

5. Coordinate Geometry and Transformations Checkpoint review case E from Transformations on the Coordinate Plane: Which transformation preserves size and shape?

Choices: Reflection · Dilation by 2 · Stretch only x · Changing one side

Show solution
  1. Challenge: First identify exactly what the question is asking: Which transformation preserves size and shape?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Reflections are rigid motions.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
  5. Identify the diagram relationship, formula, theorem, or proof reason before calculating.

Answer: Reflection

Practice this interactively with instant feedback and an AI tutor.

Practice Coordinate Geometry and Transformations Checkpoint Take the free placement check

More Geometry lessons