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Unit III: Coordinate Geometry — Test 1

Concepts and applications · 7 questions · 17 practice marks · 40 minutes.
MCQs are scored automatically; written answers use step-wise self/teacher review.

Section A
Question 1 (1 Mark)
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Full question paper and step-wise model answers

Practice marks are not official examination weightage. Written answers require self- or teacher assessment.

Question 1 · 1 mark

The point (−3,4) lies in:

  1. Quadrant I
  2. Quadrant II
  3. Quadrant III
  4. Quadrant IV
Model answer and reasoning

(b) Quadrant II

  1. Its x-coordinate is negative and y-coordinate positive.
  2. This sign combination identifies Quadrant II.

Question 2 · 1 mark

The distance between (1,2) and (4,6) is:

  1. 3
  2. 4
  3. 5
  4. 7
Model answer and reasoning

(c) 5

  1. The horizontal and vertical changes are 3 and 4.
  2. Distance = √(3² + 4²) = 5.

Question 3 · 3 marks

Explain how assigning coordinates to a geometric point connects geometry with algebra. On a grid, mark A(2,1) and B(−1,3), and describe B relative to A.

Model answer and reasoning

B is 3 units left and 2 units above A; coordinates allow geometric properties to be expressed algebraically.

  1. Two perpendicular axes and a common origin fix the reference system.
  2. An ordered pair records signed horizontal and vertical displacements; equations can then describe sets of geometric points.
  3. B − A = (−1 − 2, 3 − 1) = (−3,2). Plot using these displacements.

Question 4 · 3 marks

Find the midpoint of A(−2,5) and B(6,−1). Verify it by comparing the displacements from each endpoint.

Model answer and reasoning

M = (2,2).

  1. Average x-coordinates: (−2 + 6)/2 = 2.
  2. Average y-coordinates: (5 − 1)/2 = 2.
  3. M − A = (4,−3) and B − M = (4,−3), so M is equally placed along the segment.

Question 5 · 3 marks

A rectangular classroom has grid vertices (0,0), (8,0), (8,6), (0,6), with 1 grid unit = 1 metre. Mark the centre and find the straight-line distance from (0,0) to the opposite corner.

Model answer and reasoning

Centre (4,3); diagonal 10 m.

  1. Draw a rectangle 8 units wide and 6 units high using the given coordinates.
  2. The centre is the midpoint of opposite corners: ((0 + 8)/2, (0 + 6)/2) = (4,3).
  3. The diagonal length is √(8² + 6²) = √100 = 10 m.
Eight by six classroom floor plan with its centre and ten-unit diagonal(0,0)(8,6)(4,3)8 m6 m

Question 6 · 3 marks

Use distances to decide whether A(0,0), B(2,2) and C(5,5) are collinear.

Model answer and reasoning

They are collinear, with B between A and C.

  1. AB = √8 = 2√2; BC = √18 = 3√2.
  2. AC = √50 = 5√2.
  3. AB + BC = AC, so equality in the triangle inequality places B on segment AC.

Question 7 · 3 marks

Check whether A(0,0), B(4,0), C(0,3) form a right-angled triangle. Identify the right-angle vertex.

Model answer and reasoning

The triangle is right-angled at A.

  1. AB² = 16 and AC² = 9.
  2. BC² = (4 − 0)² + (0 − 3)² = 25.
  3. AB² + AC² = BC²; by the converse of Pythagoras the angle opposite BC, at A, is 90°.