Content:
MA5-LIN-C-01
Find the midpoint and gradient of a line segment (interval) on the Cartesian plane
- Plot and join 2 points to form an interval on the Cartesian plane and use the interval as the hypotenuse of a right-angled triangle
- Apply the relationship gradient \( m=\frac{rise}{run} \) to find the gradient/slope of the interval joining the 2 points
- Distinguish between intervals with positive and negative gradients from a diagram
- Explain why horizontal intervals have a gradient of 0 and vertical intervals have undefined gradients using the gradient relationship
- Determine the midpoint of horizontal and vertical intervals on the Cartesian plane
- Apply the process for calculating the mean to find the midpoint, of the interval joining 2 points on the Cartesian plane
- Use graphing applications to find the midpoint and gradient/slope of an interval
Find the distance between 2 points located on the Cartesian plane
- Use the interval between 2 points as the hypotenuse of a right-angled triangle on the Cartesian plane and apply Pythagoras’ theorem to determine the length of the interval joining the 2 points
- Use graphing applications to find the distance between 2 points on the Cartesian plane
Recognise and graph equations
- Recognise that equations of the form \( y=mx+c \) represent linear relationships or straight lines
- Construct tables of values and use coordinates to graph a variety of linear relationships on the Cartesian plane, with and without digital tools
- Identify the x- and y-intercepts of lines
- Determine whether a point lies on a line using substitution
Examine parallel, horizontal and vertical lines
- Explain that parallel lines have equal gradients/slopes
- Explain why the x-axis has the equation \( y=0 \) and the y-axis has the equation \( x=0 \)
- Recognise \( y=c \) as a line parallel to the x-axis and \( x=k \) as a line parallel to the y-axis
- Graph vertical and horizontal lines
MA5-LIN-C-02
Examine the gradient/slope-intercept form
- Interpret the coefficient of \( x(m) \) as the gradient/slope, and the constant \( c \) as the y-intercept for equations of the form \( y=mx+c \)
- Find the equation of a straight line in the form \( y=mx+c \), given the gradient/slope and the y-intercept of the line
- Graph equations of the form \( y=mx+c \) by using the gradient and the y-intercept
- Determine the gradient and y-intercept of a straight line from its graph and apply these values to determine the equation of the line
- Explain the effect of increasing or decreasing the gradient with or without digital tools
- Recognise and describe linear relationships in real-life contexts
Find the equations of parallel and perpendicular lines
- Explain that 2 straight lines are perpendicular if the product of their gradients is −1
- Find the equation of a straight line that is parallel or perpendicular to another given line by applying \( y=mx+c \)
MA5-LIN-P-01
Apply formulas to find the midpoint and gradient/slope of an interval on the Cartesian plane
- Apply the formula to find the midpoint of the interval joining 2 points on the Cartesian plane: \( M(x,y)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}) \)
- Use the relationship \( m=\frac{rise}{run} \) to establish the formula for the gradient/slope \( m \) of the interval joining the 2 points \( (x_1, y_1) \) and \( (x_1, y_2) \) on the Cartesian plane: \( m=\frac{y_2-y_1}{x_2-x_1} \)
- Apply the gradient formula to find the gradient of the interval joining 2 points on the Cartesian plane
Apply the distance formula to find the distance between 2 points located on the Cartesian plane
- Apply knowledge of Pythagoras’ theorem to establish the formula for the distance \( (d) \) between the 2 points \( (x_1, y_1) \) and \( (x_1, y_2) \) on the Cartesian plane: \( d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
- Apply the distance formula to find the distance between 2 points on the Cartesian plane
Use various forms of the equation of a straight line
- Rearrange linear equations from gradient–intercept form \( (y=mx+c) \) to general form \( (ax+by+c=0) \) and vice versa
- Find the x- and y-intercepts of a straight line in any form
- Graph the equation of a straight line in any form
- Use the point–gradient form \( (y-y_1=m(x-x_1)) \) or the gradient–intercept form \( (y=mx+c) \) to find the equation of a line passing through a point \( (x_1, y_1) \), with a given gradient
- Use the gradient and the point–gradient form to find the equation of a line passing through 2 points
- Find the equation of a line that is parallel or perpendicular to a given line in any form
- Determine and justify whether 2 given lines are parallel or perpendicular
Solve problems by applying coordinate geometry formulas
- Solve problems including those involving geometrical figures by applying coordinate geometry formulas
Identify line and rotational symmetries
- Identify lines (axes) and rotational symmetry in plane shapes
- Identify line and rotational symmetry in various linear and non-linear graphs
Describe translations, reflections in an axis, and rotations through multiples of 90 degrees on the Cartesian plane, using coordinates
- Apply the notation \( P' \) to name the image resulting from applying a transformation to a point \( P \) on the Cartesian plane
- Determine and plot the coordinates for \( P' \) resulting from translating \( P \) one or more times
- Determine and plot the coordinates for \( P' \) resulting from reflecting \( P \) in either the x- or y-axis
- Determine and plot the coordinates for \( P' \) resulting from rotating \( P \) by a multiple of \( 90^\circ \) about the origin
