Free Year 9 Midpoint of a line segment Practice | Skillo

Year 9 students sitting their final NAPLAN need to be confident with midpoint of a line segment. Find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points. Skillo has targeted practice questions for this exact skill, mapped to the Australian Curriculum v9.0, free and ready to go.

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What is tested: Midpoint of a line segment

✓Find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points.
✓Questions may include word problems set in real Australian contexts
✓Both calculator and non-calculator question types are covered

Sample questions

Question 1 — Easy

The path of a rugby ball kicked by Tom during training at a Sydney oval can be modelled by the parabola y = −x² + 6x, where y is the height in metres and x is the horizontal distance in metres. Setting y = 0 gives the quadratic x² − 6x = 0. What are the x-intercepts of the parabola y = −x² + 6x, and what is the horizontal distance the ball travels before it hits the ground?

A) x-intercepts at x = 0 and x = 6; the ball travels 6 metres

B) x-intercepts at x = 3 and x = −3; the ball travels 3 metres

C) x-intercepts at x = 0 and x = −6; the ball travels 6 metres

D) x-intercepts at x = 6 and x = −6; the ball travels 12 metres

Answer: Option A is correct — Factorising x² − 6x = 0 gives x(x − 6) = 0, so x = 0 or x = 6. These are the x-intercepts of the parabola, meaning the ball lands at x = 6 metres.

Question 2 — Medium

The parabola y = x² − 7x + 10 is graphed on a number plane. Anika says the graph crosses the x-axis at x = 2 and x = 5. Kofi says the turning point of the parabola lies between these two x-intercepts. Which statement correctly describes both the x-intercepts and the x-coordinate of the turning point?

A) x-intercepts at x = 2 and x = 5; turning point at x = 3

B) x-intercepts at x = −2 and x = −5; turning point at x = −3.5

C) x-intercepts at x = 2 and x = 5; turning point at x = 3.5

D) x-intercepts at x = 1 and x = 10; turning point at x = 5.5

Answer: Factorising x² − 7x + 10 = 0 gives (x − 2)(x − 5) = 0, confirming x-intercepts at x = 2 and x = 5. The x-coordinate of the turning point is the average of the roots: (2 + 5) ÷ 2 = 3.5. Option A gives incorrect turning point x = 3, B reverses the signs of the roots, and D uses factors of 10 that sum to 11 rather than 7.

Question 3 — Hard

Zac throws a ball upward from the edge of a cliff at Noosa. The height of the ball above the base of the cliff (in metres) at time t seconds is modelled by the equation h = −t² + 4t + 12. The ball hits the ground when h = 0, which gives the quadratic t² − 4t − 12 = 0. What are the roots of this equation, and which root is the solution to the real-world problem?

A) t = 2 and t = −6; t = 2 seconds is the solution because time must be positive

B) t = 6 and t = −2; t = 6 seconds is the solution because time must be positive

C) t = −6 and t = −2; both roots are rejected because time must be positive

D) t = 6 and t = 2; both roots are valid solutions to the real-world problem

Answer: Option B is correct — Factorising t² − 4t − 12 = 0 gives (t − 6)(t + 2) = 0, so t = 6 or t = −2. Since time cannot be negative, t = −2 is rejected and t = 6 seconds is the answer.

How to use Skillo for Year 9 Numeracy

Select Year 9 and Numeracy on the home screen
Use Quick Practice — questions on midpoint of a line segment will appear as part of the session
Check the Skill Breakdown on your profile to track your accuracy on midpoint of a line segment specifically
Review explanations after each question to understand the reasoning behind correct answers

Skillo is free, requires no email or account details, and is built specifically for Australian students. Every question is mapped to the Australian Curriculum v9.0 and filtered by skill so your child practises exactly what they need.

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