Checkpoint 3 of 3 10 MC + 2 Short Answer Covers Lessons 15–20

Checkpoint 3

Coordinate Geometry & Linear Modelling. Assess your understanding of gradients, equations of lines, parallel and perpendicular relationships, and real-world linear models.

Instructions: Complete all questions. For multiple choice, select one answer and click Check. For short answer, show all working. Your responses are saved automatically.
Work mode:

Section A — Multiple Choice

2 marks each. Select the best answer.

2 marks The distance between $A(1, 3)$ and $B(5, 6)$ is:

2 marks The midpoint of $(-4, 7)$ and $(6, -3)$ is:

2 marks The gradient of the line through $(-2, 5)$ and $(4, -1)$ is:

2 marks The equation of the line with gradient $-2$ and y-intercept $5$ is:

2 marks A line parallel to $y = 3x - 4$ passing through $(2, 5)$ has equation:

2 marks The gradient of a line perpendicular to $y = -\dfrac{2}{3}x + 1$ is:

2 marks Which point lies on the line $y = 2x - 3$?

2 marks The general form of $y = \dfrac{3}{4}x - 2$ is:

2 marks A taxi charges a $8 flag fall plus $2.40 per km. The cost for $d$ km is:

2 marks In a linear model $y = 5x + 20$, the value $20$ represents:

Section B — Short Answer

Show all working. 5 marks each.

Question 11

5 marks Apply / Analyse

The points $A(-3, 2)$, $B(5, 6)$, and $C(1, -2)$ form a triangle.

(a) Show that $AB$ is parallel to $OC$ where $O$ is the origin. (3 marks)

(b) Find the length of $AC$. (2 marks)

Marking Criteria

  • 1 mark: Calculate gradient of $AB$ correctly ($m = \frac{1}{2}$)
  • 1 mark: Calculate gradient of $OC$ correctly ($m = \frac{1}{2}$)
  • 1 mark: Conclude parallel with justification (equal gradients)
  • 1 mark: Set up distance formula for $AC$
  • 1 mark: Correct answer ($\sqrt{32} = 4\sqrt{2}$ units)

Question 12

5 marks Analyse / Evaluate

A car rental company charges a daily fee plus a per-kilometre rate. For 100 km the cost is $95. For 250 km the cost is $140.

(a) Find the equation for cost $C$ in terms of distance $d$. (3 marks)

(b) Calculate the cost for 400 km and identify whether this is interpolation or extrapolation. (2 marks)

Marking Criteria

  • 1 mark: Calculate gradient (rate per km) correctly: $m = \frac{140-95}{250-100} = \frac{45}{150} = 0.30$ $/km
  • 1 mark: Find daily fee by substitution: $95 = 0.30(100) + c$ → $c = 65$
  • 1 mark: Correct equation: $C = 0.30d + 65$
  • 1 mark: Cost for 400 km: $C = 0.30(400) + 65 = 185$
  • 1 mark: Identify as extrapolation (400 km is outside the data range 100–250 km)