Coordinate Geometry: The Line - Key words
Length/Distance/Radius/ |AB|
Midpoint/Centre/M
Slope/Rate of change/m
|AB|= √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
𝑦1+𝑦
𝑥 +𝑥
2
M= ( 1 2 ,
)∗
2
2
𝑅𝑒𝑚𝑒𝑚𝑏𝑒𝑟 𝑡ℎ𝑖𝑠 𝑖𝑠 𝑎 𝑝𝑜𝑖𝑛𝑡(𝑎, 𝑏)
(a) y=mx+c … when given an equation- Get y by
itself
𝑅𝑖𝑠𝑒
(b) m= 𝑅𝑢𝑛 …….. When given a graph
𝑦 −𝑦
(c) m=𝑥2 −𝑥1 …. when given coordinates
2
Parallel
Perpendicular
Equation of a line
Intercepts
Point of intersection
Area of Triangle
1
Parallel lines have equal slopes … m1=m2
Perpendicular lines have opposite slopes (turn
upside down and change the sign)
To prove lines are perpendicular m1×m2=-1
(a) y=mx+c ….. slope and intercept
(b) 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 ) …. point and slope
Where cuts the x-axis: Let y=0
Where cuts the y-axis: Let x=0
Simultaneous Equations - find x and go back to find
y
1
(a) 2 𝑏 × 𝐻…right angled
1
(b)2 𝑎𝑏𝑠𝑖𝑛𝐶 … . 𝐴𝑛𝑔𝑙𝑒 𝑚𝑢𝑠𝑡 𝑏𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡𝑤𝑜 𝑠𝑖𝑑𝑒𝑠
1
(c) 2 |𝑥1 𝑦2 − 𝑥2 𝑦1 | …
𝑔𝑖𝑣𝑒𝑛 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠 . . 𝑂𝑛𝑒 𝑝𝑜𝑖𝑛𝑡 𝑚𝑢𝑠𝑡 𝑏𝑒 (0,0)