The tangent (of a circle) is a line that intersects the circle exactly once.

Advanced 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

In a circle, a tangent and  a __________ meet at a right angle.

The grid shows a circle, its radius and a tangent which touches the circumference at (3, -4). What is the equation of the tangent line? 

The grid shows a circle, its radius and a tangent which touches the circumference at (3,-4). The radius is a line segment of the line ...

In this graph the radius is a line segment of the line $$y=-{1\over2}x-{5\over2}$$ and the tangent is line $$y=2x-10$$. How can you tell they meet at a right angle?

Point P is such that AP : PB is in the ratio 1 : 2. Find the area of triangle OPB.

Point P is such that AP : PB is in the ratio 5 : 1. The area of triangle OAP is {{ }} square units.

Two lines are perpendicular if their gradients are the negative __________ of one another.

Match each line with a line that is perpendicular to it.

What is the equation of the straight line that goes through the coordinates (-5, -23) and (3, 17)?

Find the coordinates of the point P when AP : PB is in the ratio 1 : 5.

What is the coordinate of C when AB : BC is in the ratio 1 : 2?

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