Answer with Explanation

Name:

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 d = √[(x2−x1)^2 + (y2−y1)^2], show steps, 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 Answers — Show work and explain

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

Final answer (circle your exact result):

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 and explain your rounding.

Final answer:

7. If the distance between (x, 1) and (4, 5) is 5, find all possible values of x. Show algebraic steps and explain how you solved for x.

Final answer:

8. Sketch the points A(1,1), B(1,5), and C(5,1) in the box below. Which two points are farthest apart? Explain using distance reasoning (show calculations).

Final answer (write which points and why):

Dyslexia-friendly reading option: Read each question slowly. Underline both point coordinates before calculating. Use a ruler or highlight numbers to track changes.

Differentiation strategies: For support, compute horizontal and vertical distances first or provide graph paper with points pre-plotted. For challenge, give both exact radical form and decimal approximations.

Extension activity: Choose three points you invent. Compute all three pairwise distances, show work, and determine whether the three points form a right triangle using the Pythagorean relationship. Write a one-sentence conclusion.