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Coordinate geometry
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Created by
Elsa Sims
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Cards (17)
gradient
of line is
y2-y1
/
x2-x1
midpoint
is
(
x
1
+
x
2
)
/
2
,
(
y
1
+
y
2
)
/
2
(x1+x2)/2 , (y1+y2)/2
(
x
1
+
x
2
)
/2
,
(
y
1
+
y
2
)
/2
length
of a line is the
square root
of
(
x
2
−
x
1
)
2
+
(x2-x1)^2+
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
(y2-y1)^2
(
y
2
−
y
1
)
2
equation
of
straight line
is y=
mx+c
equation
of line with
gradient
and
coords
is
y
−
y
1
=
y-y1=
y
−
y
1
=
m
(
x
−
x
1
)
m(x-x1)
m
(
x
−
x
1
)
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
x
2
+
x^2+
x
2
+
y
2
=
y^2=
y
2
=
R
2
R^2
R
2
equation
of circle with
centre
(a,b) and
radius
r is
(
x
−
a
)
2
+
(x-a)^2+
(
x
−
a
)
2
+
(
y
−
b
)
2
=
(y-b)^2=
(
y
−
b
)
2
=
R
2
R^2
R
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
r
1
+
r1+
r
1
+
r
2
>
d
r2>d
r
2
>
d
then circles intersect at 2 points
if
r
1
+
r1+
r
1
+
r
2
<
d
r2<d
r
2
<
d
there are no points of
intersection
if
r
1
+
r1+
r
1
+
r
2
=
r2=
r
2
=
d
d
d
they touch externally
if
r
2
−
r
1
=
r2-r1=
r
2
−
r
1
=
d
d
d
then
circles
touch externally