Tales by Dots and Lines — Practice

Question 1

In which quadrant does (−4, 3) lie?

Accepted Answer

✦ Answer: Q2 (top-left). Negative x means left of y-axis; positive y means above x-axis.

Question 2

In a pie chart of 1000 people surveyed, 250 voted for Party A. What's the angle for Party A?

Accepted Answer

✦ Answer: (250/1000) × 360° = 90°.

Question 3

Plot points (1, 3), (2, 6), (3, 9). Find the equation of the line.

Accepted Answer

Step 1 — Identify pattern.
  y/x = 3/1 = 6/2 = 9/3 = 3 (constant)
  Direct proportion: y = 3x.

Step 2 — Verify all points.
  (1, 3): 3(1) = 3 ✓
  (2, 6): 3(2) = 6 ✓
  (3, 9): 3(3) = 9 ✓

Step 3 — Line characteristics.
  Passes through origin (0, 0)
  Slope = 3
  Equation: y = 3x

✦ Answer: The equation of the line is y = 3x. Direct proportion with slope 3.

Question 4

A bar graph shows monthly sales (in lakh ₹): Jan 4, Feb 6, Mar 8, Apr 5, May 7, Jun 10. Find: (a) Total annual sales (first half), (b) Average monthly sales, (c) Best month.

Accepted Answer

Part (a) — Total.
  4 + 6 + 8 + 5 + 7 + 10 = 40 lakh

Part (b) — Average.
  Average = Total / 6 = 40/6 ≈ 6.67 lakh per month

Part (c) — Best month.
  Highest bar = June (10 lakh).

✦ Answer: (a) Total = ₹40 lakh. (b) Average ≈ ₹6.67 lakh/month. (c) June was the best month with ₹10 lakh sales.

Question 5

A family's monthly budget is ₹40,000. Construct a pie chart with the following categories: Food ₹12,000, Rent ₹10,000, Education ₹8,000, Savings ₹6,000, Other ₹4,000.

Accepted Answer

Step 1 — Compute angles.
  • Food: (12000/40000) × 360° = 108°
  • Rent: (10000/40000) × 360° = 90°
  • Education: (8000/40000) × 360° = 72°
  • Savings: (6000/40000) × 360° = 54°
  • Other: (4000/40000) × 360° = 36°

Step 2 — Verify.
  Total: 108 + 90 + 72 + 54 + 36 = 360° ✓

Step 3 — Construction (description).
  Draw a circle. Use a protractor to mark sectors:
  • Largest sector (Food) = 108°
  • Then Rent (90°)
  • Then Education (72°)
  • Then Savings (54°)
  • Smallest (Other) = 36°
  Colour each sector differently and label.

Step 4 — Percentages (for reference).
  Food 30%, Rent 25%, Education 20%, Savings 15%, Other 10%.

✦ Answer: Angles: Food 108°, Rent 90°, Education 72°, Savings 54°, Other 36°. Sum = 360°.

Practice — Tales by Dots and Lines

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