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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:

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Gradient between two points

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The gradient between two points is determined by the ratio of vertical change to horizontal change.

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The formula for finding the gradient of a line is:

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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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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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For more practice or to ask an expert for help on this section see: www.everythingmaths.co.za Shortcode: EMACV

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