Mathematics K–10 - Stage 5 - Linear relationships C (Path) | NSW Curriculum

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Linear relationships C (Path)

MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
MA5-LIN-P-01
describes and applies transformations, the midpoint, gradient/slope and distance formulas, and equations of lines to solve problems (Path: Adv)

Linear relationships C (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

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 $m = \frac{r i s e}{r u n}$ to establish the formula for the gradient/slope ( $m)$ of the interval joining the 2 points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ 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 $(x_{2}, y_{2})$ 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 $(y = m x + c)$ to general form $(a x + b y + c = 0)$ 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 ( $y = m x + c$ ) to find the equation of a line passing through a point $(x_{1}, y_{1})$ , with a given gradient $m$
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

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 $90^{°}$ about the origin

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Life Skills

K–10Mathematics K–10 Syllabus