Define a perpendicular bisector .

A perpendicular bisector of a line segment cuts the line segment in half at a right angle .

What are the two key pieces of information needed to find the equation of a straight line ?

To find the equation of a straight line , you need the gradient of the line and the coordinates of a point on the line.

How do you find the gradient of a perpendicular bisector ?

The gradient of a perpendicular bisector can be found by dividing -1 by the gradient of the original line segment. It is the negative reciprocal of the gradient of the original line segment.

What does the notation [AB] represent in coordinate geometry?

The notation [AB] represents the line segment between points A and B .

True or False? In exams, you should always use degrees unless otherwise indicated.

False. In exams, you should use radians unless otherwise indicated.

Define the term arc .

An arc is a part of the circumference of a circle.

Define the term radius .

The radius is the distance from the centre of a circle to the circumference . Radius also refers to a line segment from the centre of a circle to the circumference .

Define the term sector .

A sector is a part of a circle enclosed by two radii and an arc .

True or False? The perimeter of a sector is just the arc length .

False. The perimeter of a sector is the arc length plus two radii .

True or False? The area of a major sector is always larger than the area of a minor sector in the same circle .

True. The area of a major sector is always larger than the area of a minor sector in the same circle .

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FrontCoordinate Geometry
State the expression for the midpoint of two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .
FrontCoordinate Geometry
What is the formula for calculating the distance between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ ?
BackCoordinate Geometry
The distance between two points is calculated using the formula, $d = \sqrt{({(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2})}$
Where:
$d$ is the distance between two points
$(x_{1}, y_{1})$ is the set of coordinates for a known point
$(x_{2}, y_{2})$ is the set of coordinates for another known point
This is given in your exam formula booklet.
FrontCoordinate Geometry
What is the formula for finding the gradient of a line between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ ?
BackCoordinate Geometry
The gradient can be found using the formula $m = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})}$
Where:
$m$ is the gradient of the line
$(x_{1}, y_{1})$ is the set of coordinates for a known point
$(x_{2}, y_{2})$ is the set of coordinates for another known point
This is given in your exam formula booklet.

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Cards in this collection (28)

State the expression for the midpoint of two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .
The expression for the midpoint of two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ .
This is given in your exam formula booklet.
What is the formula for calculating the distance between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ ?
The distance between two points is calculated using the formula, $d = \sqrt{({(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2})}$
Where:
- $d$ is the distance between two points
- $(x_{1}, y_{1})$ is the set of coordinates for a known point
- $(x_{2}, y_{2})$ is the set of coordinates for another known point
This is given in your exam formula booklet.
What is the formula for finding the gradient of a line between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ ?
The gradient can be found using the formula $m = \frac{(y_{2} - y_{1})}{(x_{2} - x_{1})}$
Where:
- $m$ is the gradient of the line
- $(x_{1}, y_{1})$ is the set of coordinates for a known point
- $(x_{2}, y_{2})$ is the set of coordinates for another known point
This is given in your exam formula booklet.
Define a perpendicular bisector.
A perpendicular bisector of a line segment cuts the line segment in half at a right angle.
True or False?
Two lines are perpendicular if the product of their gradients is -1.
True.
Two lines are perpendicular if the product of their gradients is -1.
E.g. if a line has a gradient of 2, then a line that is perpendicular to it will have a gradient of $- \frac{1}{2}$ as $2 \times - \frac{1}{2} = - 1$ .
What are the two key pieces of information needed to find the equation of a straight line?
To find the equation of a straight line, you need the gradient of the line and the coordinates of a point on the line.
How do you find the gradient of a perpendicular bisector?
The gradient of a perpendicular bisector can be found by dividing -1 by the gradient of the original line segment.
It is the negative reciprocal of the gradient of the original line segment.
After finding the gradient of a perpendicular, how do you use a point on the line to find its full equation?
After finding the gradient of a perpendicular, you can use a point on the line to find its full equation by:
- Substituting the coordinates of the point and the gradient into the gradient-intercept form $y = m x + c$ (then solving to find the value of $c$ )
- Or substituting the coordinates of the point and the gradient into the point-gradient form $y - y_{1} = m (x - x_{1})$ (then rearranging that equation into whatever form is required)
It is often easiest to substitute into the point-gradient form.
What is the point-gradient form of a straight line equation?
The point-gradient form is $y - y_{1} = m (x - x_{1})$ .
Where:
- $m$ is the gradient of the line
- $(x, y)$ is the set of coordinates for any point on the line
- $(x_{1}, y_{1})$ is the set of coordinates for a known point on the line
This is given in your exam formula booklet.
True or False?
$a x + b y + d = 0$ is the equation of a straight line.
True.
The equation of a straight line is usually given in one of three main forms:
- $y = m x + c$ ,
- $y - y_{1} = m (x - x_{1})$ ,
- or $a x + b y + d = 0$ .
These are all given in your formula booklet.
What does the notation [AB] represent in coordinate geometry?
The notation [AB] represents the line segment between points A and B.
What are radians?
Radians are a way of measuring of angles as an alternative to degrees.
1 radian is the angle in a sector with radius 1 and arc length 1.
What is the symbol for radians?
Radians are indicated with $^{c}$ but it is more typical to see $rad$ . Sometimes, if the angle includes $π$ , then no symbol is used as the use of radians is implied.
Degrees will always be indicated with º.
True or False?
$2 π rad = 180 º$ .
False.
$2 π rad = 360 º$ .
How do you convert an angle from radians to degrees?
To convert from radians to degrees, multiply by $\frac{180}{π}$ .
How do you convert an angle from degrees to radians?
To convert from degrees to radians, multiply by $\frac{π}{180}$ .
True or False?
In exams, you should always use degrees unless otherwise indicated.
False.
In exams, you should use radians unless otherwise indicated.
Define the term arc.
An arc is a part of the circumference of a circle.
Define the term radius.
The radius is the distance from the centre of a circle to the circumference.
Radius also refers to a line segment from the centre of a circle to the circumference.
Define the term sector.
A sector is a part of a circle enclosed by two radii and an arc.
True or False?
A minor arc has an angle at the centre less than 180° $(π rad)$ .
True.
A minor arc has an angle at the centre less than 180° $(π rad)$ .
State the equation for the length of an arc when working with degrees.
The equation for the length of an arc, when working with degrees, is $l = \frac{θ}{360} \times 2 π r$
Where:
- $l$ is the length of the arc
- $θ$ is the angle of the sector in degrees
- $r$ is the radius of the sector
This formula is in the exam formula booklet.
State the equation for the length of an arc when working with radians.
The equation for the length of an arc, when working with radians, is $l = r θ$
Where:
- $l$ is the length of the arc
- $θ$ is the angle of the sector in radians
- $r$ is the radius of the sector
This formula is in the exam formula booklet.
True or False?
The perimeter of a sector is just the arc length.
False.
The perimeter of a sector is the arc length plus two radii.
State the equation for the area of a sector, when working with degrees.
The equation for the area of a sector, when working with degrees, is $A = \frac{θ}{360} \times π r^{2}$
Where:
- $A$ is the area of the sector
- $θ$ is the angle of the sector in degrees
- $r$ is the radius of the sector
This formula is in the exam formula booklet.
State the equation for the area of a sector, when working with radians.
The equation for the area of a sector, when working with radians, is $A = \frac{1}{2} r^{2} θ$
Where:
- $A$ is the area of the sector
- $θ$ is the angle of the sector in radians
- $r$ is the radius of the sector
This formula is in the exam formula booklet.
What is the fraction used to calculate sector area or arc length, when working with degrees?
The fraction used to calculate sector area or arc length is the angle at the centre divided by 360°, $\frac{θ}{360}$ .
True or False?
The area of a major sector is always larger than the area of a minor sector in the same circle.
True.
The area of a major sector is always larger than the area of a minor sector in the same circle.

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Geometry Toolkit (DP IB Applications & Interpretation (AI))

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Cards in this collection (28)

1. Number & Algebra

Number Toolkit

Exponentials & Logs

Sequences & Series

Financial Applications

Complex Numbers

Further Complex Numbers

Matrices

Eigenvalues & Eigenvectors

2. Functions

Linear Functions & Graphs

Further Functions & Graphs

Modelling with Functions

Functions Toolkit

Transformations of Graphs

Modelling with Logarithmic, Logistic & Piecewise Functions

3. Geometry & Trigonometry

Geometry Toolkit

Geometry of 3D Shapes

Trigonometry

Trigonometric Identities & Equations

Voronoi Diagrams

Matrix Transformations

Vector Properties

Vector Equations of Lines

Modelling with Vectors

Graph Theory

4. Statistics & Probability

Statistics Toolkit

Correlation & Regression

Non-linear Regression

Probability

Probability Distributions

Random Variables

Binomial Distribution

Normal Distribution

Combinations of Normal Distributions & Sample Mean Distributions

Poisson Distribution

Hypothesis Testing using the Chi-squared Distribution

Hypothesis Testing for Population Parameters

Transition Matrices & Markov Chains

5. Calculus

Differentiation

Further Differentiation

Integration

Further Integration

Kinematics

Differential Equations

Coupled & Second Order Differential Equations