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Pythagoras Coordinates

A self marking exercise on the application of Pythagoras' Theorem.

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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 red points?

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

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

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

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

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What is the length of the line segment joining (5, 0) and (3, 5)?

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What is the length of the line segment joining (2, 3) and (-3, -1)?

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What is the length of the line segment joining (-6, 4) and (3, -1)?

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What is the length of the line segment joining (5, 3) and (5, -3)?

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Ant
A very small ant began a journey at the origin, (0, 0), then walked in a straight line to (-5, 1) before turning and walking in a straight line to (7, -1). What was the total length of the ant's journey?

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Pythagoras Coordinates Diagram
The diagram above shows a line segment that begins at the point (-5,0) and ends where it intersects the y-axis at p. Find the value of p if the length of the line segment is 21 units.

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

The point A is at (-1, 1) and the point B is at (7, -5). Another point, C, is found such that the angle AĈB is a right angle. If the length of AC is 8 units, find the length of BC.

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Check

 

Instructions

Try 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.

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Description of Levels

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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 right-angled triangles.

Three Dimensions - Three dimensional Pythagoras and trigonometry questions

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Pythagoras' Theorem

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.

Pythagoras' Theorem

You may have learned the theorem using letters to stand for the lengths of the sides. The corners (vertices) of the right-angled triangle is labelled with capital (upper case) letters. The lengths of the sides opposite them are labelled with the corresponding small (lower case) letters.

Pythagoras' Theorem

Alternatively the sides of the right-angled triangle may me named using the capital letters of the two points they span.

Pythagoras' Theorem

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 right-angled 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 right-angled 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.

Example

Pythagoras Example

AB2 = AC2 - BC2
AB2 = 4.72 - 4.12
AB2 = 22.09 - 16.81
AB2 = 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.

Rotations

The right-angled triangles could be long and thin or short and not so thin.

Different proportions
Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.

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