Year 9 Maths • AC9M9A03 • Authored homework
Gradient, distance, midpoint and line modelling
Use coordinates to calculate gradient, distance and midpoint, and use these ideas to model linear relationships on the Cartesian plane. Show working, use correct notation and check reasonableness.
Part A
Short-answer questions
Find the gradient between (1, 3) and (5, 11).
Find the midpoint of A(2, 6) and B(8, 10).
Use the distance formula to find the distance between (0, 0) and (3, 4).
State whether the line through (2, 5) and (6, 5) is horizontal, vertical or sloping.
Write the gradient formula in words or symbols.
Find the equation of a line with gradient 3 and y-intercept -2.
Explain what a gradient of 0 means.
Find the y-intercept of y = -2x + 7.
Correct this error: gradient from (1, 2) to (4, 8) is (4 - 1)/(8 - 2).
Describe a real context where gradient represents a rate of change.
Part B
Long-answer questions
Calculate the gradient, midpoint and distance between A(-2, 3) and B(4, 11). Show all working.
A road on a map goes from (1, 2) to (7, 5). Interpret the gradient and distance in the context of the map.
Find the equation of a line passing through (0, 4) and (3, 10), then check using both points.
Compare two line segments using gradient and distance. Decide which is steeper and which is longer.
A phone plan has a fixed cost and a cost per GB. Model it with a linear equation and explain the gradient and intercept.
Use midpoint to find the centre of a rectangular garden with opposite corners at (2, 1) and (10, 7).
Explain why the distance formula is connected to Pythagoras. Use a diagram or example.
A student swaps x and y changes when finding gradient. Explain the error and solve a correct example.
Create a coordinate problem involving two locations, then calculate distance, midpoint and gradient.
Write a full solution for a real-world linear modelling problem, including equation, graph features and interpretation.
Part C
Research and understanding task
Research one use of coordinate geometry in maps, design, sport tracking, robotics or games. Create a coordinate model, calculate gradient, midpoint or distance, and explain what the answer means.