Everything Maths, Grade 10. Chapter 8: Analytical geometry.

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8. Analytical Geometry
Grade 10

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Distance between two points
● A point is an ordered pair of numbers written as (x; y).
● Distance is a measure of the length between two points.
● The formula for finding the distance between any two points is:
Gradient of a line
● The gradient of a line is determined by the ratio of vertical change to horizontal change.
● The formula for finding the gradient of a line is:

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Straight lines
● A straight line is a set of points with a constant gradient between any two of the points.
● The standard form of the straight line equation is y = mx + c.
● The equation of a straight line can also be written as

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Parallel and perpendicular line
● If two lines are parallel, their gradients are equal.
● If two lines are perpendicular, the product of their gradients is equal to −1.
● For horizontal lines the gradient is equal to 0.
● For vertical lines the gradient is undefined.

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Mid-point of a line
The formula for finding the mid-point between two points is:

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