Core Chapter 1: Straight Lines Flashcards
How is a line’s gradient measured?
rise/run = y₂- y₁/x₂- x₁
What are a line’s x-intercepts and y-intercepts?
x-intecept: y=0
y-intercept: x=0
What are the 2 different types of lines?
Parallel lines: same gradient
(m₁=m₂)
Perpendicular lines: gradients are negative reciprocals of each other
(m₁= -1/m₂)
What are the 3 different forms of an equation of a straight line?
1) Gradient-intercept form
(y = mx + c)
- When the gradient (m) and y-intercept (c) is known
2) Point-gradient form
(y-y₁/x-x₁=m)
(y-y₁=m(x-x₁)
- When coordinates of 1 point (x₁, y₁) and the gradient (m) is known
3) General form (ax + by + d = 0)
- Rearranged using other forms
What is a perpendicular bisector?
How can the equation of the perpendicular bisector be found?
Perpendicular bisector:
1) Perpendicular to the line
(gradient is negative reciprocal to the line’s gradient)
2) Passes through the line’s midpoint (x₁+x₂/2, y₁+y₂/2)
Equation of a perpendicular bisector:
1) Find mid-point of the line (intersection between the line and its perpendicular bisector)
2) Find gradient of the line
3) Find gradient of the perpendicular bisector
4) Apply point-gradient form