Formula for finding out the gradient of a line when no co-ordinates are known

m = tanƟ (where Ɵ is the angle between the line and the positive direction of the x-axis)

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What is collinearity?

When three points all lie on the same line

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How do we show that 3 points are collinear?

1) M/ab = M/bc - shows that the line AB is parallel to BC. 2) Share a common point B so A,B,C must be collinear

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Formula for the midpoint of a line

(x₁+x₂) ÷ 2 , (y₁+y₂) ÷ 2

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Formula for perpendicular lines

M₁ = 1/M or M₁ x M₂

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Forms of a straight line

y=mx+c / ax+by+c=0

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Equation of a straight line

y-b = m(x-a) (where (a,b) is equal to any point on the line and m is the gradient)

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How do you find out if a point on a line?

Substitute the point into the equation of the line

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How do you find out where a line cuts the co-ordinate axis?

substitute x=0 into the equation of the line to find out where it cuts out the y-axis. substitute y=0 into the equation of the line to find out where it cuts out the x-axis.

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What is the median?

A line from a vertex to the midpoint of the base

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What is the altitude?

A perpendicular line from a vertex to the base (not a midpoint)

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What is a perpendicular bisector?

A line that cuts another line into two equal parts at an angle of 90°

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What is the definition of concurrent?

Lines are concurrent if they all pass through the same point

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How can we find the point of intersection of 2 lines?

By using simultaneous equations

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How do we show that lines are concurrent?

Solve 2 of the equations simultaneously to set the point of intersection and then use that point to find out if it is on the 3rd line

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Other cards in this set

Card 2

Front

Distance formula

Back

AB = √(x₂-x₁)² + (y₂-y₁)²

Card 3

Front

Formula for finding out the gradient of a line when no co-ordinates are known

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