Unit 3 - Straight lines and circles Flashcards
Distance between two points (straight line)
(x2 - x1)^2 + (y2 - y1)^2
All of this square rooted .
Midpoint of a straight line
(x1 + x2) / 2, (y1 + y2) / 2
Gradient of a straight line
(y2 - y1) / (x2 - x1)
Gradient of parallel lines
Parallel lines have the same gradient
Gradient of perpendicular lines
The gradients of perpendicular lines are negative reciprocals. They multiply to make -1.
Formula of a straight line
(y - y1) = m(x - x1)
Equation of a circle
(x-a)^2 + (y-b)^2 = r^2
centre = (a,b)
radius = r
Tangent
Perpendicular to the radius of the circle. A straight line that touches the circle at just one point.
Perpendicular bisector
The perpendicular bisector from the centre to a chord bisects the chord.
Right-angled triangle in a circle
If the triangle passes through the centre of the circle and all three corners touch the circumference, then the triangle is right-angled.
