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Unit Test 3: Coordinate Geometry

Class 10 Mathematics (Standard)

Time: 1 Hour Max. Marks: 30

General Instructions:

  • The question paper consists of 15 questions divided into 4 sections: A, B, C, and D.
  • Section A: 6 MCQs of 1 mark each.
  • Section B: 4 Short Answer questions of 2 marks each.
  • Section C: 4 Short Answer questions of 3 marks each.
  • Section D: 1 Case Study based question of 4 marks.
  • Use of calculators is not permitted.
SECTION A (1 Mark Each)
[1] 1. The distance of the point P(3, 4) from the origin is:
[1] 2. The mid-point of the line segment joining the points (-2, 8) and (-6, -4) is:
[1] 3. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is:
[1] 4. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the:
[1] 5. The distance between points (a, b) and (-a, -b) is:
[1] 6. If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of 'a' is:
SECTION B (2 Marks Each)
[2] 7. Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4).
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[2] 8. Find a relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (-3, 4).
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[2] 9. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.
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[2] 10. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, –3) and B is (1, 4).
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SECTION C (3 Marks Each)
[3] 11. Find the coordinates of the points of trisection of the line segment joining (4, –1) and (–2, –3).
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[3] 12. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (–1, 4) and (–2, –1) taken in order.
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[3] 13. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (-1, -2), (1, 0), (-1, 2), (-3, 0).
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[3] 14. Find the coordinates of the point which divides the line segment joining A(-2, 2) and B(2, 8) into four equal parts.
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SECTION D (Case Study - 4 Marks)
[4] 15. Case Study: Sports Day

To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in the figure (assume A is origin (0,0), AB is x-axis, AD is y-axis).

Niharika runs 1/4th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5th the distance AD on the 8th line and posts a red flag.

(i) What are the coordinates of the green flag? (1 Mark)
(ii) What is the distance between both the flags? (2 Marks)
(iii) If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag? (1 Mark)
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TOTAL SCORE

0 / 6 (MCQ)

(Subjective answers submitted for review)

Solution Key (MCQs)

Q1. (c) 5

Distance = √(3² + 4²) = √(9+16) = √25 = 5.

Q2. (a) (-4, 2)

Mid-point = ((-2-6)/2, (8-4)/2) = (-8/2, 4/2) = (-4, 2).

Q3. (a) ±4

Distance² = (4-1)² + (p-0)² = 25 ⇒ 9 + p² = 25 ⇒ p² = 16 ⇒ p = ±4.

Q4. (d) IV Quadrant

x = (1(3)+2(7))/3 = 17/3 (+ve), y = (1(4)+2(-6))/3 = -8/3 (-ve). (+, -) is IV Quadrant.

Q5. (a) 2√(a² + b²)

Dist = √((a - -a)² + (b - -b)²) = √((2a)² + (2b)²) = √(4a² + 4b²) = 2√(a² + b²).

Q6. (b) -12

x-coordinate of mid-point: a/3 = (-6-2)/2 = -4 ⇒ a = -12.