Maths revision course by Miriam Hanks

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Presentation transcript:

Maths revision course by Miriam Hanks Coordinate Geometry Coordinate geometry is the study of shapes and lines. When is it used in real life? Maths revision course by Miriam Hanks

Coordinate Geometry in real life Architects use it to construct buildings, bridges and roads Car designers use CAD Astrophysicists use it to find the distances between planets Medical imaging techniques such as a CAT scanners use it Maths revision course by Miriam Hanks

Maths revision course by Miriam Hanks Gradients The gradient m is the slope. For straight lines, use: or m = 2 m = 1 m = 0 m =tan θ Maths revision course by Miriam Hanks

Parallel and perpendicular Parallel lines: same gradient Gradients flip and change sign Perpendicular lines: Maths revision course by Miriam Hanks

Equations of straight lines The equation of a straight line is: or y – b = m(x – a) y = mx + c Maths revision course by Miriam Hanks

Maths revision course by Miriam Hanks Midpoint formula To find the midpoint: find the mean of the two x-coordinates, and then the mean of the two y-coordinates Midpoint Midpoint Maths revision course by Miriam Hanks

Maths revision course by Miriam Hanks Distance formula The distance formula uses Pythagoras with the CHANGE in the horizontal and vertical distances. (x2, y2) y2 – y1 (x1, y1) x2 – x1 Maths revision course by Miriam Hanks

Maths revision course by Miriam Hanks Medians A median of a triangle goes from one point to the midpoint of the line opposite: Maths revision course by Miriam Hanks

Maths revision course by Miriam Hanks Altitudes An altitude of a triangle goes from one point straight down to meet the opposite side at a right-angle: Maths revision course by Miriam Hanks

Perpendicular bisectors A perpendicular bisector cuts a line at its midpoint AND at right-angles and so would not necessarily go through the corner of the triangle. Maths revision course by Miriam Hanks