Coordinate Plane Distance

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Date:

📚 Part 1: Learning Targets & Multiple Choice

I can... find distances between two points on the coordinate plane using horizontal/vertical reasoning and the distance formula.

Success criteria: I can identify horizontal or vertical distances, apply the distance formula d = √[(x2-x1)^2 + (y2-y1)^2], and give exact or rounded answers as required.

1. What is the distance between (2, 3) and (7, 3)?

√26

2. What is the distance between (−1, 4) and (−1, −2)?

√20

3. What is the distance between (1, 2) and (4, 6)?

√13

4. Which pair of points has a distance of √20?

(−1, 0) and (3, 4)

(0, 0) and (4, 2)

(2, 1) and (5, 5)

(−2, −2) and (2, 2)

✏️ Part 2: Short Answer (show work)

5. Find the exact distance between (−3, −2) and (4, 1). Show your work.

6. The city map uses a coordinate grid with coordinates in miles. Find the distance between (0, 0) and (2, 3). Give your answer rounded to the nearest tenth.

7. If the distance between (x, 1) and (4, 5) is 5, find all possible values of x. Show steps.

8. Sketch (by hand) the points A(1,1), B(1,5), and C(5,1). Which two points are farthest apart? Explain using distance reasoning.

🧭 Supports, Differentiation & Extensions

Dyslexia-friendly reading option: Read each question slowly. Underline the two point coordinates before calculating. Use a colored ruler or highlighter to track numbers.

Differentiation strategies: For students who need support, provide graph paper with the points pre-plotted or let them compute horizontal/vertical distances first. For students who need challenge, ask them to find distances in 3 steps: exact radical form, simplified radical form, and decimal approximation.

Extension activity: Choose three points you invent. Compute all three pairwise distances and determine whether these form a right triangle (use the Pythagorean relationship).

Reminder: Show your work in the math-work-boxes and circle your final answers in the short-answer-boxes.