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

Ratios in line segments on coordinate axes

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

Halfway between the two end points of a line segment is the ...

Three points A, B and P are plotted. If AP : PB is in the ratio of 1 : 1 then P is the {{}} of AB.

Find the coordinates of the point P when AP : PB is in the ratio 3 : 1.

Find the coordinates of the point P when AP : PB is in the ratio 1 : 4.

Find the coordinates of the point P when AP : PB is in the ratio 3 : 2.

Two Oak pupils share 30 sweets in the ratio of 1 : 1. What proportion of the sweets does the second pupil receive?

£280 is divided in the ratio of 1 : 4. Which calculation can be used to find the larger share?

8640 grams is divided in the ratio of 3 : 5. How much is in the smaller share?

What number is exactly in the middle of -17 and 60?

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