Name: ___________________________ Date: ______________ Class: ____________
LEVEL 2 · ENRICHMENT

Integers & the Coordinate Plane

Standards: 6.NS.C.5 (Positive/Negative) · 6.NS.C.6 (Number Line/Plane) · 6.NS.C.7 (Absolute Value) · 6.NS.C.8 (Graphing)

Directions: Solve each challenge and show all work. For "Explain" prompts, justify your reasoning in complete sentences. Finish with the Stretch Problem.

Challenge Problems

1. Point A is at (−4, 3) and Point B is at (5, 3). Find the distance between them and the midpoint. MULTI-STEP

2. A rectangle has vertices at (−3, 4), (5, 4), (5, −2), and (−3, −2). Find its perimeter and area. MULTI-STEP

3. Arrange from least to greatest: |−7|, −4, |3|, −|−5|, 0 REASONING

4. A triangle has vertices at (0, 0), (6, 0), and (6, 8). Find its perimeter. CHALLENGE

Use the Pythagorean theorem for the slanted side.

5. A point reflected across the x-axis lands at (3, −7). What were its original coordinates? REASONING

6. Point P(−2, 5) is reflected across the y-axis to get P′, then P′ is reflected across the x-axis to get P″. Find P″. MULTI-STEP

7. A delivery drone starts at (0, 0), flies to (4, 0), then to (4, 3). How far is it from the start in a straight line? REAL-WORLD

8. Which is farther from zero: −15 or 12? EXPLAIN

Explain how absolute value helps you decide.

9. Plot any four points that form a square with an area of 16 square units. List your four ordered pairs. OPEN-ENDED

10. A submarine is at −80 feet. A fish is at −35 feet. Which is deeper, and how far apart are they? REAL-WORLD

Explain Your Reasoning

11. Two students disagree. One says "−10 is greater than −2 because 10 is greater than 2." Is this correct? Explain who is right and why, using a number line in your reasoning. WRITE

★ Stretch Problem

A square has two opposite corners at (−2, −2) and (4, 4). Find the coordinates of the other two corners, the side length, the perimeter, and the area. Justify how you found the missing corners.

Answer Key

  1. Distance = 9 units (|−4| + |5|); Midpoint = (0.5, 3)
  2. Length 8, width 6; Perimeter = 28, Area = 48
  3. −5, −4, 0, 3, 7 (that is −|−5|, −4, 0, |3|, |−7|)
  4. 24 units — legs 6 and 8, hypotenuse √(36+64) = 10; 6+8+10 = 24
  5. (3, 7) — the y-coordinate flips
  6. (2, −5) — x flips then y flips
  7. 5 units — √(4² + 3²) = √25 = 5
  8. −15 — |−15| = 15 > |12| = 12, so −15 is farther from zero
  9. Sample: (0,0), (4,0), (4,4), (0,4) — side 4, area 16
  10. Submarine is deeper; distance = |−80 − (−35)| = 45 feet
  11. The second student is right; −2 is closer to zero (to the right) on the number line, so −2 > −10
  12. Stretch: other corners (4, −2) and (−2, 4); side = 6, perimeter = 24, area = 36