The midpoint of a line segment is halfway between the two end points.

Problem solving with linear graphs

Maths

The work on gradient in this unit is expanded further in the future unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In the prior unit, pupils drew a linear graph from its equation and related the features of the graph to its equation. In this unit, pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

Linear graphs

What is the coordinate of the midpoint of the line segment AB?

Point P has coordinates (3, -8) and point Q has coordinates (10, -2). What is the coordinate of the midpoint of PQ?

Point A has coordinates (6, 2) and B has coordinates (12, 0). Line L has equation $$y = 2x - 5.$$ What is the equation of the line parallel to L which passes through the midpoint of AB?

The line segments AB and BC have the same gradient.

The line segments AB and DC have the same gradient.

The line segments AD and BC have the same gradient. 

The line segment AB has a smaller gradient than the line segment BC.

If shape ABCD is a parallelogram, which of these statements would have to be true?

The side lengths are not all the same length. 

The midpoint of AC is different to the midpoint of BD.

Jacob plots four points A, B, C on a graph. Jacob says he can join the points to form a parallelogram. Why is Jacob incorrect? 

Which of these coordinates are on the line $$x = 2$$?

Which of these lines passes through the coordinates (2, 8) and (5, 8)?

{{}} lines are straight lines which are always the same non-zero distance apart. 

The gradient of the line passing through (5, 5) and (9, -3) is {{}}. 

Starter Quiz