Fichas
Coordinate Geometry Basics
Fichas del conjunto (11)
- 1Gradient = ...y2-y1 / x2-x1
(change in y / change in x) - 2Distance = ...root((x2-x1)^2)+(y2-y1)^2)
(Pythagoras) - 3Midpoint = ...(x1+x2)/2 , (y1+y2)/2
(coordinate) - 4Equations of lines = ...y=mx+c
y-y1=m(x-x1) - 5Parallel lines have....The same gradients
- 6If lines are perpendicular, they....Multiply to make -1
m1 = -1/m2
m1m2 = -1 - 7Find parallel of 2x+5y-7=0 through (-1,3). Give in form ax+by+c=0.Rearrange to get y alone, so y=-2/5x+7/5. Now we sub in the point, so 3=-2/5 x -1 + c. This can be simplified to give c=13/5. Now we put this back into y=mx+c to get y=-2/5+13/5.
- 8What is the equation for direct proportionality?y = kx
- 9What is the equation of inverse proportionality?y = k/x
- 10If we have the equation of a circle and a tangent and we need to find the radius, what steps should we take?1. Create simultaneous equation and set equal to 0
2. Now we can use the discriminant as we know it must = 0 (as tangents only touch the circle in one place) to find r - 11If we have a perpendicular bisector of a line, we know the bisector passes through the....Midpoint of the line