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maths
pure
coordinate geometry - lines
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Created by
eve siddaway
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Cards (10)
gradient formula
y
2
−
y
1
/
x
2
−
x
1
y2-y1/x2-x1
y
2
−
y
1/
x
2
−
x
1
straight line equations
y
=
y=
y
=
m
x
+
mx+
m
x
+
c
c
c
or
a
x
2
+
ax^2+
a
x
2
+
b
x
+
bx+
b
x
+
c
=
c=
c
=
0
0
0
equation to find equation of a
line
y
−
y
1
=
y-y1=
y
−
y
1
=
m
(
x
−
x
1
)
m(x-x1)
m
(
x
−
x
1
)
find points where line meets x
axis
make y=0
solve for x
find where line meets y axis
make
x=0
solve
for y
parralel lines
have
same
gradient
perpendicular lines
gradients are negative reciprocals of each other, multiply to make -1
midpoint
of
line formula
[
(
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
)]
mean
of x and
y
values
length between two points
Pythagoras
theorem
a
2
+
a^2+
a
2
+
b
2
=
b^2=
b
2
=
c
2
c^2
c
2
or
s
q
u
a
r
e
r
o
o
t
(
x
2
−
x
1
)
2
+
square root(x2-x1)^2+
s
q
u
a
reroo
t
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
(y2-y1)^2
(
y
2
−
y
1
)
2
find
intersection
of lines
finding a point where
x
and
y
satisfies both equations
can solve by
simultaneous
equations,
substituting
one into the other or make
equal
to each other