Linear Relationships C

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Linear relationships C (Path) | NSW Curriculum Website

• MA5-LIN-P-01 describes and applies transformations, the midpoint, gradient/slope and distance formulas, and equations of lines to solve problems

📖 Prior Knowledge

Content	Prerequisite relationships
Geometric Measure B	- Describe coordinate changes under transformation → Transform points on the Cartesian plane
Two-dimensional Spatial Structure A	- Investigate symmetry of quadrilaterals → Identify line and rotational symmetry
Linear Relationships	- Plot points on the Cartesian plane → Transform points on the Cartesian plane
Linear Relationships A	- Find the gradient of an interval → Apply the gradient formula - Find the midpoint of an interval → Apply the midpoint formula - Find the distance between two points → Apply the distance formula
Linear Relationships B	- Interpret gradient–intercept form → Convert between gradient–intercept and general form - Find a line’s equation from gradient and intercept → Find a line’s equation using point–gradient form - Find equations of parallel and perpendicular lines → Find and test parallel and perpendicular lines in any form - Find perpendicular gradients and classify line pairs → Solve problems using coordinate geometry formulas
Equations C	- Change the subject of a formula → Convert between gradient–intercept and general form

Apply formulas to find the midpoint and gradient slope of an interval on the Cartesian plane.pdf

• Apply the formula to find the midpoint of the interval joining 2 points on the Cartesian plane: $M\left(x,y\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$
• Use the relationship $m=\frac{\text{rise}}{\text{run}}$ 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.pdf

• 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: $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$
• 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.pdf

• Rearrange linear equations from gradient–intercept form $y=mx+c$ to general form $ax+by+c$ 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 $m$
• 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.pdf

• Solve problems including those involving geometrical figures by applying coordinate geometry formulas

Identify line and rotational symmetries.pdf

• 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.pdf

• Apply the notation $P^{\prime }$ to name the image resulting from applying a transformation to a point $P$ on the Cartesian plane
• Determine and plot the coordinates for $P^{\prime }$ resulting from translating $P$ one or more times
• Determine and plot the coordinates for $P^{\prime }$ resulting from reflecting $P$ in either the $x$- or $y$-axis
• Determine and plot the coordinates for $P^{\prime }$ resulting from rotating $P$ by a multiple of 90° about the origin