#3.1
Know and use the definition of a gradient
#3.2
Know the relationship between the gradients of parallel and perpendicular lines
Show that A (0, 2), B (4, 6) and C (10, 0) form a right- angled triangle
#3.3
Use Pythagoras' theorem to calculate the distance between two points
#3.4
Use ratio to find the coordinates of a point on a line given the coordinates of two other points
Including midpoint
#3.5
The equation of a straight line
\( y = mx + c \) and \( y - y_1 = m (x - x_1) \)
and other forms
Including interpretation of the gradient and y-intercept from the equation
#3.6
Draw a straight line from given information
#3.7
Understand that \( x^2 + y^2 = r^2 \) is the equation of a circle with centre \((0, 0)\) and radius \(r\)
Including writing down the equation of a circle given centre (0, 0) and radius
The application of circle geometry facts where appropriate:
the angle in a semi-circle is 90°;
the perpendicular from the centre to a chord bisects the chord;
the angle between tangent and radius is 90°;
tangents from an external point are equal in length.
#3.8
Understand that \( (x - a)^2 + (y - b)^2 = r^2 \) is the equation of a circle with centre \((a, b) \) and radius \(r\)
Including writing down the equation of any circle given centre and radius
#3.9
The equation of a tangent at a point on a circle