P1.2 - Coordinate geometry in the (x, y) plane

Equation of a straight line, To include: including the forms (i) the equation of a line through two given points y − y = m(x − x) and 1 1 (ii) the equation of a line parallel (or perpendicular) to a ax + by + c = 0. given line through a given point.; For example, the line perpendicular to the line 3x + 4y = 18 through the point (2, 3) has equation y − 3 = 4 (x − 2).

Use equation of a straight line to connect the rule to the data and decision in the question.

This matters because equation of a straight line determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply equation of a straight line to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.

Conditions for two straight lines to be parallel or perpendicular to each other.

Use parallel and perpendicular lines to connect the rule to the data and decision in the question.

This matters because parallel and perpendicular lines determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply parallel and perpendicular lines to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Parallel and perpendicular lines is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.