Finding the area of a triangle using coordinates and working... Show more
Mathematics5 views·Updated May 23, 2026·2 pagesUnderstanding the Area of a Triangle
C
Cayla Martin@caylamartin
1
of 2
Area of a Triangle Using Coordinates
When you need to find the area of a triangle using three coordinate points, there's a straightforward method that works every time. The key is to simplify your work by moving one point to the origin.
Here's the process: first, move one of your three points to (0,0) by subtracting its coordinates from all three points. Then move the other two points in exactly the same direction. This keeps the triangle's shape and area identical.
Once you've repositioned the points, use the coordinate area formula with your two remaining points. For example, if you have points at (5,3) and (2,-6) after moving, the area equals |5×(-6) - 2×3| ÷ 2 = 18 square units.
Quick Tip: Always take the absolute value of your final calculation - area can never be negative!
2
of 2
Equation of a Line and Perpendicular Lines
Finding the equation of a line becomes manageable when you know what you need: one point on the line and the slope (m). The standard formula y - y₁ = m is your starting point for most problems.
Perpendicular lines have slopes that are negative reciprocals of each other. If one line has slope 2, a perpendicular line will have slope -1/2. This relationship is crucial for solving exam questions.
When working with midpoints and perpendicular lines, calculate the midpoint first using the midpoint formula, then find the slope of the original line. Remember to flip the sign and reciprocal for your perpendicular slope.
Exam Strategy: Always convert your final answer to the format requested - whether that's y = mx + c or ax + by + c = 0.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Mathematics
8MathematicsAlgebra
Algebra
5th Year91
MathematicsAlgebra 2
Algebra notes focusing on the factor theorem, completing the square, -b formula, graphs of polynomials
5th Year130
MathematicsSolving Equations
This section focuses on solving one-step and two-step linear equations to find the value of an unknown variable.
1st Year131
MathematicsIntroduction to Probability
This topic introduces basic probability concepts, including calculating the probability of simple events and understanding the difference between experimental and theoretical probability.
2nd Year81
MathematicsMaths jc algebra
Maths jc
1st Year230
MathematicsNatural Numbers and Integers
Students will learn about positive whole numbers, zero, and negative whole numbers, and how to add, subtract, multiply, and divide them correctly.
1st Year131
MathematicsDifferential Calculus
Calculus is a topic that comes up nearly everywhere on your maths LC. This is just starter notes that could be useful end of 5th year or start of 6th year
5th Year271
MathematicsArithmetic sequences and series
With examples
5th Year130
Most popular content
9
IrishIrish oral questions and answers
Questions and answers for the leaving cert oral
5th Year4254
IrishIrish oral questions
Outline of oral questions
5th Year2055
EnglishKey Quotes : Sive
Key Quotes and explanations: Sive
6th Year2822
IrishIníon- le hÁine Durkin
Aine Durkin’s poem, Iníon: Themes & summary
5th Year850
IrishIrish poetry 2027
Iníon + Dínit an Bhróin
5th Year1133
IrishLC HL notes- Iníon (poem)
Includes poem in English and Irish, theme, key words & phrases
5th Year2284
IrishGaeilge Grammar Office
All the basics you need to know on Irish grammar.
6th Year1053
EnglishCultural Context : Shawshank Redemption : Sive : Small Things Like These
Comparative Study : Cultural Context : Shawshank Redemption, Sive and Small Things Like These
6th Year1420
IrishAn Gaeilge Aiste
Irish Language essay
6th Year1310
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user
Mathematics5 views·Updated May 23, 2026·2 pagesUnderstanding the Area of a Triangle
C
Cayla Martin@caylamartin
Finding the area of a triangle using coordinates and working with line equations are essential skills in coordinate geometry. These techniques will help you tackle exam questions involving shapes on graphs and understanding how lines relate to each other.
1
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Area of a Triangle Using Coordinates
When you need to find the area of a triangle using three coordinate points, there's a straightforward method that works every time. The key is to simplify your work by moving one point to the origin.
Here's the process: first, move one of your three points to (0,0) by subtracting its coordinates from all three points. Then move the other two points in exactly the same direction. This keeps the triangle's shape and area identical.
Once you've repositioned the points, use the coordinate area formula with your two remaining points. For example, if you have points at (5,3) and (2,-6) after moving, the area equals |5×(-6) - 2×3| ÷ 2 = 18 square units.
Quick Tip: Always take the absolute value of your final calculation - area can never be negative!
2
of 2Sign up to see the content. It's free!
- Access to all documents
- Improve your grades
- Join milions of students
Equation of a Line and Perpendicular Lines
Finding the equation of a line becomes manageable when you know what you need: one point on the line and the slope (m). The standard formula y - y₁ = m is your starting point for most problems.
Perpendicular lines have slopes that are negative reciprocals of each other. If one line has slope 2, a perpendicular line will have slope -1/2. This relationship is crucial for solving exam questions.
When working with midpoints and perpendicular lines, calculate the midpoint first using the midpoint formula, then find the slope of the original line. Remember to flip the sign and reciprocal for your perpendicular slope.
Exam Strategy: Always convert your final answer to the format requested - whether that's y = mx + c or ax + by + c = 0.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Mathematics
8MathematicsAlgebra
Algebra
5th Year91
MathematicsAlgebra 2
Algebra notes focusing on the factor theorem, completing the square, -b formula, graphs of polynomials
5th Year130
MathematicsSolving Equations
This section focuses on solving one-step and two-step linear equations to find the value of an unknown variable.
1st Year131
MathematicsIntroduction to Probability
This topic introduces basic probability concepts, including calculating the probability of simple events and understanding the difference between experimental and theoretical probability.
2nd Year81
MathematicsMaths jc algebra
Maths jc
1st Year230
MathematicsNatural Numbers and Integers
Students will learn about positive whole numbers, zero, and negative whole numbers, and how to add, subtract, multiply, and divide them correctly.
1st Year131
MathematicsDifferential Calculus
Calculus is a topic that comes up nearly everywhere on your maths LC. This is just starter notes that could be useful end of 5th year or start of 6th year
5th Year271
MathematicsArithmetic sequences and series
With examples
5th Year130
Most popular content
9IrishIrish oral questions and answers
Questions and answers for the leaving cert oral
5th Year4254
IrishIrish oral questions
Outline of oral questions
5th Year2055
EnglishKey Quotes : Sive
Key Quotes and explanations: Sive
6th Year2822
IrishIníon- le hÁine Durkin
Aine Durkin’s poem, Iníon: Themes & summary
5th Year850
IrishIrish poetry 2027
Iníon + Dínit an Bhróin
5th Year1133
IrishLC HL notes- Iníon (poem)
Includes poem in English and Irish, theme, key words & phrases
5th Year2284
IrishGaeilge Grammar Office
All the basics you need to know on Irish grammar.
6th Year1053
EnglishCultural Context : Shawshank Redemption : Sive : Small Things Like These
Comparative Study : Cultural Context : Shawshank Redemption, Sive and Small Things Like These
6th Year1420
IrishAn Gaeilge Aiste
Irish Language essay
6th Year1310
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5App Store
4.7/5Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan SiOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha KlichAndroid user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
AnnaiOS user