#5.2
Know and be able to use the relationship between the gradients of parallel lines and perpendicular lines.
For parallel lines \(m_1 = m_2\).
For perpendicular lines \(m_1m_2 = -1\).
#5.4
Be able to find the coordinates of the midpoint of a line segment joining two points.
#5.5
Be able to form the equation of a straight line.
Including \(y - y_1 = m(x - x_1)\) and \(ax + by + c = 0\)
#5.6
Be able to draw a line given its equation.
By using gradient and intercept or intercepts with axes as well as by plotting points.
#5.7
Be able to find the point of intersection of two lines.
By solution of simultaneous equations.
#5.8
Be able to use straight line models.
In a variety of contexts; includes considering the assumptions that lead to a straight line model.
#5.9
Be able to find the point(s) of intersection of a line and a curve or of two curves.
#5.11
Understand and use the equation of a circle in the form \((x - a)^2 + (y - b)^2 = r^2\).
Includes completing the square to find the centre and radius.
#5.12
Know and be able to use the following properties:
• the angle in a semicircle is a right angle;
• the perpendicular from the centre of a circle to a chord bisects the chord;
• the radius of a circle at a given point on its circumference is perpendicular to the tangent to the circle at that point.
These results may be used in the context of coordinate geometry.
#5.14
Be able to convert between cartesian and parametric forms of equations.
When converting from cartesian to parametric form, guidance will be given as to the choice of parameter.
#5.16
Be able to find the gradient of a curve defined in terms of a parameter by differentiation.
\(\dfrac{dy}{dx} = \dfrac{\Bigg(\dfrac{dy}{dt}\Bigg)}{\Bigg(\dfrac{dx}{dt}\Bigg)}\)
[Excludes: Second and higher derivatives.]
#5.17
Be able to use parametric equations in modelling.
Contexts include kinematics and projectiles in mechanics. Including modelling with a parameter with a restricted domain.