Pythagoras CoordinatesA self marking exercise on the application of Pythagoras' Theorem. 
Each square on the grid represents one unit. Type your answers to three significant figures if it is not a whole number.
What is the length of the line joining the two blue points? 

What is the length of the line joining the two maroon points? 

What is the length of the line joining the two yellow points? 

What is the length of the line joining the two orange points? 

What is the length of the line joining the two pink points? 

What is the length of the line segment joining (6, 1) and (0, 5)? 

What is the length of the line segment joining (8, 0) and (1, 2)? 

What is the length of the line segment joining (1, 0) and (6, 4)? 

What is the length of the line segment joining (7, 0) and (7, 3)? 





Finally here's a challenging question to make you really think hard! 

InstructionsTry your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help. When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file. 



Transum.orgThis web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available. Please contact me if you have any suggestions or questions. 
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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician? Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield: "I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information." Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School: "This is a great memory aid which could be used for formulae or key facts etc  in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is  my pupils love it! 
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Go MathsLearning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school. Maths MapAre you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.  
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Level 0  A 'whole number only' introductory set of questions
Level 1  Finding the hypotenuse
Level 2  Finding a shorter side
Level 3  Mixed questions
Level 4  Pythagoras coordinates
Level 5  Mixed exercise
Level 6  More than one triangle
Level 7  Harder exercise
Exam Style questions requiring an application of Pythagoras' Theorem and trigonometric ratios to find angles and lengths in rightangled triangles.
Three Dimensions  Three dimensional Pythagoras and trigonometry questions
More on this topic including lesson Starters, visual aids, investigations and selfmarking exercises.
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See the National Curriculum page for links to related online activities and resources.
The area of the square on the hypotenuse of a right angled triangle is equal to the sum of the areas of the squares on the two shorter sides.
You may have learned the theorem using letters to stand for the lengths of the sides. The corners (vertices) of the rightangled triangle is labelled with capital (upper case) letters. The lengths of the sides opposite them are labelled with the corresponding small (lower case) letters.
Alternatively the sides of the rightangled triangle may me named using the capital letters of the two points they span.
As triangle can be labelled in many different ways it is probably best to remember the theorem by momorising the first diagram above.
To find the longest side (hypotenuse) of a rightangled triangle you square the two shorter sides, add together the results and then find the square root of this total.
To find a shorter side of a rightangled triangle you subtract the square of the other shorter side from the square of the hypotenuse and then find the square root of the answer.
AB^{2} = AC^{2}  BC^{2}
AB^{2} = 4.7^{2}  4.1^{2}
AB^{2} = 22.09  16.81
AB^{2} = 5.28
AB = √5.28
AB = 2.3m (to one decimal place)
The diagrams aren't always the same way round. They could be rotated by any angle.
The rightangled triangles could be long and thin or short and not so thin.
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