This course studies the straight line using coordinates. It starts with the inclination and slope of a line and the slope conditions for parallel and perpendicular lines and collinear points. It then derives every standard form of the equation of a line: point-slope, two-point, slope-intercept, intercept, normal, symmetric and general forms, and shows how to move between them. Later lessons find the point where two lines meet, the angle between them, concurrent lines, the perpendicular distance from a point to a line, the foot of the perpendicular, the image of a point, and the orthocentre and circumcentre of a triangle.
Middle Years
Coordinate Geometry (Straight Lines)
3-week course.
- 8 lessons
Overview
Lessons
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Inclination and slope of a line
The inclination of a line, its slope as tan θ, the slope from two points, and what the sign of the slope says about the line.
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Parallel and perpendicular lines and collinear points
Equal slopes for parallel lines, product of slopes −1 for perpendicular lines, collinear points, and testing triangles and quadrilaterals.
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Point-slope and two-point forms
Lines parallel to the axes, the equation of a line from a point and its slope or from two points, and medians and perpendicular bisectors.
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Slope-intercept and intercept forms
The forms y = mx + c and x/a + y/b = 1, reading slope and intercepts, and the area a line cuts off with the axes.
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Normal, symmetric and general forms
The normal form x cos α + y sin α = p, the general form ax + by + c = 0 and converting between forms, and points at a given distance along a line.
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Intersection and angle between two lines
The point where two lines meet, the angle between them, lines parallel or perpendicular to a given line, and concurrent lines.
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Distance of a point from a line
The perpendicular distance formula, the distance between parallel lines, altitudes and areas of triangles, and which side of a line a point lies on.
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Foot of the perpendicular, image and centres of a triangle
The foot of the perpendicular from a point to a line, the image of a point in a line, and the orthocentre and circumcentre of a triangle.