17 Questions
What is the formula to find the midpoint of a line segment between two points?
((x1 + x2)/2, (y1 + y2)/2)
What is the formula to find the distance between two points?
√((x2 - x1)^2 + (y2 - y1)^2)
What is the condition for two lines to be parallel?
They have the same gradient but different y-intercepts
What is the gradient of a line that is perpendicular to a line with gradient m?
-1/m
What is the equation of the perpendicular bisector of a line segment?
The line that passes through the midpoint of the line segment
What is the common characteristic of a family of parallel lines?
They have the same gradient but different y-intercepts
What is the condition for a pair of equations to have no solution?
The equations have the same slope and different y-intercepts
If a football team scores three more goals than behinds, how can we express the number of goals in terms of the number of behinds?
Number of goals = Number of behinds + 3
When solving a system of equations, what is the purpose of adding or subtracting the equations?
To eliminate one of the variables
What is the first step in solving the simultaneous equations and?
Subtract the two equations to eliminate one variable
What is the cost of a single book if the cost of 2 pens and 1 book is $15, and the cost of 3 pens and 1 book is $22?
$7
What is the goal of solving a system of simultaneous equations?
To find the intersection point of the two equations
What is the suitable method to solve simultaneous equations if one pronumeral is the subject of one equation?
Substitution
Mark is 3 times as old as Julie. If the difference in their ages is 10 years, what is Mark's age?
20 years
In a junior football game, if the Tigers scored 2 tries and 6 goals with a total of 28 points, and the Crows scored 3 tries and 4 goals with a total of 27 points, what is the number of points awarded for each goal?
4 points
What is the ratio of the width to the length of a rectangle?
No information provided
A student purchased 10 books and 5 pens for $22.50. If the cost of one book and one pen is $3.15, what is the cost of the 10 books?
$20.55
Study Notes
Coordinate Geometry Practice Test
- The practice test consists of 30 questions covering various topics in coordinate geometry.
Midpoint of a Line Segment
- The midpoint of a line segment between two points (x1, y1) and (x2, y2) is given by ((x1 + x2)/2, (y1 + y2)/2).
Distance between Two Points
- The distance between two points (x1, y1) and (x2, y2) is given by √((x2 - x1)^2 + (y2 - y1)^2).
Gradient and Equations of Lines
- The gradient of a line perpendicular to a line with equation y = mx + c is -1/m.
- The equation of a line perpendicular to y = mx + c and passing through a point (x1, y1) is y - y1 = (-1/m)(x - x1).
Simultaneous Equations
- Simultaneous equations can be solved using substitution or elimination methods.
- To eliminate a variable, you can add or subtract the equations.
Applications of Coordinate Geometry
- Coordinate geometry can be used to solve problems involving distance, midpoint, and gradient in real-world scenarios, such as football games and stationery shop costs.
- The technique of solving simultaneous equations can be used to find unknown values in a system.
Practice your coordinate geometry skills with this 30-question test, covering topics such as midpoint of line segments, distance between points, and more. Improve your understanding of coordinate geometry concepts and prepare for your exam. This test is designed to help you assess your knowledge and identify areas for improvement.
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