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Cards (40)
How do parallel lines behave?
They
never meet
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What is the gradient of parallel lines?
They have the same gradient
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What defines perpendicular lines?
They cross at a
right angle
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What is the angle at which perpendicular lines intersect?
90°
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What happens to the gradient of a line that is perpendicular to another?
It must be
negative
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What is the gradient of the purple line perpendicular to y = 2x + 1?
-1/2
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How do you calculate the gradient of the purple line?
Change in Y
over
change in X
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What is the gradient of the line perpendicular to y = 3x + 2?
-1/3
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What is the relationship between the gradients of perpendicular lines?
They are
negative reciprocals
of each other
Their
product
equals
-1
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What is the reciprocal of 2?
1/2
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What is the reciprocal of 3?
1/3
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What is the reciprocal of a fraction like 2/3?
3/2
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How do you find the reciprocal of a decimal like 0.9?
Convert to
fraction
, then
flip
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How do you show two lines are perpendicular?
Multiply their
gradients
to get
-1
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What do you conclude if the product of two gradients is -1?
The lines are
perpendicular
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What do you conclude if the product of -2/3 and 3/2 is -1?
The lines are
perpendicular
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How do you determine if two lines are perpendicular?
Multiply their
gradients
to get
-1
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How do you find the gradient of L2 if L1's gradient is -4?
Take the
negative reciprocal
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What form do we write the equation of L2?
y =
mx + C
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How do you find the gradient of L2 from L1's gradient of
3
4
\frac{3}{4}
4
3
?
Take the
negative reciprocal
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What is the gradient of L2 if L1's gradient is
3
4
\frac{3}{4}
4
3
?
-
4
3
\frac{4}{3}
3
4
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How do you find C using the point (6, -1)?
Substitute into the
equation
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What is the formula to find the gradient between two coordinates?
\(
\frac{y_2 - y_1}{x_2 - x_1}\)
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How do you find the gradient of line AB using coordinates A(1, 5) and B(3, 6)?
Substitute into the gradient
formula
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What is the gradient of line AB from the coordinates given?
1
2
\frac{1}{2}
2
1
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What is the gradient of the line perpendicular to AB?
-2
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What is the equation of the line perpendicular to AB?
y = -2x + C
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How do you find C using the point (1, 5)?
Substitute into the
equation
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What is the value of C after substituting (1, 5)?
-3
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What is the final equation of the line perpendicular to AB?
y = -2x - 3
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What is the gradient of line AB in the last example?
5
2
\frac{5}{2}
2
5
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How do you find the gradient of the line perpendicular to AB?
Take the
negative reciprocal
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What is the gradient of the line perpendicular to AB?
-
2
5
\frac{2}{5}
5
2
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How do you write the equation of the line perpendicular to AB?
y = -
2
5
\frac{2}{5}
5
2
x + C
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How do you find C using the point (10, -2)?
Substitute into the
equation
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What is the value of C after substituting (
10
,
-2
)
?
2
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What is the final equation of the line perpendicular to AB?
y = -
2
5
\frac{2}{5}
5
2
x + 2
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What are the steps to find the equation of a line perpendicular to another line given a point?
Find the
gradient
of the first line.
Calculate the
negative reciprocal
for the perpendicular line's gradient.
Use the point to find the
Y-intercept
(C).
Write the equation in the form y = mx + C.
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What are the key concepts in determining if two lines are perpendicular?
Calculate
gradients
of both lines.
Their
product
must equal -1.
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What is the process for finding the gradient from two coordinates?
Use the
formula
:
y
2
−
y
1
x
2
−
x
1
\frac{y_2 - y_1}{x_2 - x_1}
x
2
−
x
1
y
2
−
y
1
Substitute the coordinates into the formula.
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