Part 1: Multiple-Choice Questions

Choose the correct answer for each question.

1. What is the gradient of the line passing through (2, 3) and (6, 11)?

1

2

3

4

2. Which equation represents a line with gradient 3 and y-intercept −2?

y = 3x + 2

y = −3x − 2

y = 3x − 2

y = 2x + 3

3. What is the midpoint of the line segment joining (−4, 6) and (8, 2)?

(2, 4)

(4, 2)

(−2, 4)

(2, −4)

4. Which pair of lines is perpendicular?

y = 2x + 1 and y = 2x − 4

y = −2x + 1 and y = 2x − 4

y = 2x + 1 and y = ½x − 4

y = −½x + 1 and y = 2x − 4

Part 2: Skills and Calculations

Show all working. Give exact answers where appropriate.

5. Find the distance between A(−3, 4) and B(5, −2).

6. Find the equation of the line passing through (1, 5) and (4, 14). Write your answer in the form y = mx + b.

7. Determine whether the points P(−2, 1), Q(2, 9) and R(5, 15) are collinear. Justify your answer.

8. The line 2x + y = 8 intersects the x-axis and y-axis. Find both intercepts and state the coordinates of the point of intersection.

Part 3: Application and Graphing

9. A taxi fare is modelled by the equation C = 2.40d + 4.50, where C is the cost in dollars and d is the distance in kilometres.

a) State the gradient and explain what it represents.

b) State the y-intercept and explain what it represents.

c) Calculate the cost of a 7.5 km journey.

10. On the coordinate grid below, plot A(−4, −1), B(2, 5) and C(6, 1). Join the points to form triangle ABC. Calculate the gradient of AB and determine whether triangle ABC is right-angled.

Coordinate Geometry Test

Coordinate Geometry Test

Part 1: Multiple-Choice Questions

Part 2: Skills and Calculations

Part 3: Application and Graphing

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