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Mathematics questions, chapter 7
Nama / NameKelas / ClassTarikh / Date

Coordinates

42 marks. Use Practice to check each answer as you go, or Exam to answer everything first. Show your working for Section B. Give lengths that are not whole numbers correct to 2 decimal places.

Section A: objective questions

10 marks
Choose the correct answer. Each question carries 1 mark.
1

Question 1

Which statement about the Cartesian plane is correct?
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B
The x-axis is horizontal and the y-axis is vertical; they cross at right angles at the origin (0, 0). A point is written (x, y) with x first.
For the teacher: Remembering, low difficulty, standard 7.1.1
Textbook p. 123
2

Question 2

In which quadrant is the point (4, −6)?
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D
x is positive and y is negative, which is (x, −y): the 4th quadrant. The 1st has both positive; the 2nd has x negative; the 3rd has both negative.
For the teacher: Understanding, low difficulty, standard 7.1.1
Textbook p. 124
3

Question 3

Diagram 1 shows the line PQ on a Cartesian plane. One square on the x-axis is 5 units. What is the distance PQ?
Horizontal line PQ with P at x = −10 and Q at x = 20, both at the same height between y = 2 and y = 4; the x-axis is labelled in steps of 5 and the y-axis in steps of 2
Diagram 1
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A
PQ covers 20 − (−10) = 30 units, which is 6 squares × 5 units. 6 forgets the scale; 25 and 15 come from mistakes with the negative sign.
For the teacher: Applying, low difficulty, standard 7.1.2
Textbook p. 124
4

Question 4

The points A(1, 2) and B(4, 6) are joined. What is the length AB?
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B
AB = √[(4 − 1)² + (6 − 2)²] = √(9 + 16) = √25 = 5 units. 7 is 3 + 4 (the sides added); 25 forgets the square root.
For the teacher: Applying, low difficulty, standard 7.1.3
Textbook p. 127
5

Question 5

Calculate the distance between (−3, 4) and (5, −2).
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A
Horizontal: 5 − (−3) = 8. Vertical: −2 − 4 = −6, squared 36. √(64 + 36) = √100 = 10. √28 comes from subtracting the squares (64 − 36) instead of adding; 14 is 8 + 6.
For the teacher: Applying, medium difficulty, standard 7.1.3
Textbook p. 128
6

Question 6

The distance between A(−1, 2) and B(5, k) is 10 units, and k is greater than 2. Find the value of k.
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C
(5 − (−1))² + (k − 2)² = 100 gives 36 + (k − 2)² = 100, so (k − 2)² = 64 and k − 2 = ±8. k = 10 or k = −6. Since k is greater than 2, k = 10.
For the teacher: Analysing, high difficulty, standard 7.1.4
Textbook p. 129
7

Question 7

Find the midpoint of the line joining (2, 5) and (8, 1).
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B
((2 + 8)/2, (5 + 1)/2) = (5, 3). (10, 6) forgets to halve; (3, 2) is half the differences.
For the teacher: Applying, low difficulty, standard 7.2.3
Textbook p. 135
8

Question 8

What is the midpoint of (−8, 5) and (2, −11)?
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D
((−8 + 2)/2, (5 + (−11))/2) = (−6/2, −6/2) = (−3, −3). (5, −8) uses subtraction, which gives half the distances; (−6, −6) forgets to halve.
For the teacher: Applying, low difficulty, standard 7.2.3
Textbook p. 135
9

Question 9

The straight line joining (−8, 3) and (s, 3) has the midpoint (1, u). Find the values of s and u.
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C
(−8 + s)/2 = 1 gives s = 10. (3 + 3)/2 = 3 gives u = 3. s = 9 comes from forgetting to double the midpoint (1 − (−8)), and u = 6 forgets to halve.
For the teacher: Applying, medium difficulty, standard 7.2.4
Textbook p. 137
10

Question 10

The vertices of a triangle are A(−3, 0), B(3, 0) and C(0, 4). What is its perimeter?
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B
AB = 6 (same y). AC = √(3² + 4²) = 5 and BC = √(3² + 4²) = 5. Perimeter = 6 + 5 + 5 = 16 units. 12 is the area, not the perimeter.
For the teacher: Analysing, medium difficulty, standard 7.3.1
Textbook p. 141

Section B: structured questions

32 marks
Answer all questions. Show your working.
11

Question 11

State the distance between each pair of points.
[1 mark] (a)(2, −3) and (7, −3)
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Tick each point you got.
[1 mark] (b)(−4, 5) and (−4, −1)
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 7.1.2
Textbook p. 126
12

Question 12

Diagram 2 shows three points A, B and C on a Cartesian plane. AC is parallel to the y-axis and CB is parallel to the x-axis.
Point C(−2, 3) with a vertical line of 5 units up to A(−2, a) and a horizontal line of 7 units to the right to B(b, 3)
Diagram 2
[2 marks] (a)AC = 5 units. Find the value of a.
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Tick each point you got.
[2 marks] (b)CB = 7 units. Find the value of b.
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A and C share the x-coordinate; B and C share the y-coordinate.
Tick each point you got.
For the teacher: Applying, low difficulty, standard 7.1.2
Textbook p. 126
13

Question 13

Diagram 3 shows the points P(−2, 1) and Q(4, 9).
Line from P(−2, 1) to Q(4, 9) on a Cartesian plane
Diagram 3
[2 marks] (a)State the horizontal distance and the vertical distance between P and Q.
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Tick each point you got.
[2 marks] (b)Calculate the length PQ.
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 7.1.3
Textbook p. 128
14

Question 14

Diagram 4 shows triangle ABC with A(1, 2), B(5, 2) and C(3, 6).
Triangle with A(1, 2) and B(5, 2) on a horizontal base and C(3, 6) above
Diagram 4
[3 marks] (a)Show that triangle ABC is an isosceles triangle.
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Tick each point you got.
[2 marks] (b)Calculate the perimeter of the triangle.
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√20 = 4.47 correct to 2 decimal places.
Tick each point you got.
For the teacher: Analysing, medium difficulty, standard 7.1.4
Textbook p. 129
15

Question 15

The distance between P(−2, 3) and Q(m, 7) is 5 units, where m is greater than 0. Calculate the value of m.
[4 marks] (a)Form an equation and solve it to find m.
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Tick each point you got.
For the teacher: Analysing, medium difficulty, standard 7.1.4
Textbook p. 129
16

Question 16

Find the midpoint of the line joining each pair of points.
[1 mark] (a)(2, −4) and (8, 6)
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Tick each point you got.
[1 mark] (b)(−7, 0) and (3, −5)
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Tick each point you got.
For the teacher: Applying, low difficulty, standard 7.2.3
Textbook p. 135
17

Question 17

M(1, −2) is the midpoint of the straight line AB. The coordinates of A are (−5, 4). Calculate the coordinates of B.
[3 marks] (a)Find the coordinates of B.
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Check: ((−5 + 7)/2, (4 + (−8))/2) = (1, −2).
Tick each point you got.
For the teacher: Applying, low difficulty, standard 7.2.4
Textbook p. 137
18

Question 18

Diagram 5 shows a rectangle KLMN with K(1, 2), L(7, 2) and N(1, 10).
Rectangle with K(1, 2) and L(7, 2) at the bottom and N(1, 10) at the top left; M is the top right corner
Diagram 5
[1 mark] (a)State the coordinates of M.
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Tick each point you got.
[2 marks] (b)Calculate the length of the diagonal LN.
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Tick each point you got.
[1 mark] (c)Find the midpoint of LN.
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Tick each point you got.
[1 mark] (d)Mei says that the midpoint of the other diagonal, KM, is the same point as the midpoint of LN. Is Mei right?
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Yes
Midpoint of KM = ((1 + 7)/2, (2 + 10)/2) = (4, 6). The diagonals of a rectangle bisect each other.
For the teacher: Evaluating, medium difficulty, standard 7.3.1
Textbook p. 141
19

Question 19

A line joins two points. The midpoint of the line is (3, −1).
[2 marks] (a)Write down the coordinates of one possible pair of end points. Neither point may lie on an axis.
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Tick each point you got.
[1 mark] (b)Show by calculation that your points have the midpoint (3, −1).
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Tick each point you got.
For the teacher: Creating, high difficulty, standard 7.2.3
Textbook p. 135