Coordinate geometry

    Cards (17)

    • gradient of line is y2-y1/x2-x1
    • midpoint is (x1+x2)/2,(y1+y2)/2(x1+x2)/2 , (y1+y2)/2
    • length of a line is the square root of (x2x1)2+(x2-x1)^2+(y2y1)2(y2-y1)^2
    • equation of straight line is y=mx+c
    • equation of line with gradient and coords isyy1=y-y1=m(xx1)m(x-x1)
    • parallel lines have the same gradient
    • perpendicular line have gradients that multiply to make -1
    • equation of circle with centre of (0,0) and radius r is x2+x^2+y2=y^2=R2R^2
    • equation of circle with centre (a,b) and radius r is (xa)2+(x-a)^2+(yb)2=(y-b)^2=R2R^2
    • a tangent has one point of intersection
    • a perpendicular bisecter of a chord will go through the centre of a circle
    • a tangent to a circle is perpendicular to the radius of the circle at the point of intersection
    • the angle in a semi circle is always a right angle
    • if r1+r1+r2>dr2>d then circles intersect at 2 points
    • if r1+r1+r2<dr2<d there are no points of intersection
    • if r1+r1+r2=r2=dd they touch externally
    • if r2r1=r2-r1=dd then circles touch externally