Unit 1 - Outcome 1 - Straight Lines

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Formula for parallel lines
m₁ = m₂ = m₃
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Distance formula
AB = √(x₂-x₁)² + (y₂-y₁)²
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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

Back

Preview of the front of card 3

Card 4

Front

What is collinearity?

Back

Preview of the front of card 4

Card 5

Front

How do we show that 3 points are collinear?

Back

Preview of the front of card 5
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