Year 9

Pythagoras's theorem on the Cartesian plane

Year 9

Pythagoras's theorem on the Cartesian plane

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Lesson details

Key learning points

  1. In this lesson, we will learn how to use Pythagoras's theorem on the Cartesian plane to help you find the distance between two given points.

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7 Questions

Q1.
Which side the the hypotenuse of the below triangle?
An image in a quiz
Correct answer: m
n
p
Q2.
The digram shows a right-angled triangle. What is the length of the hypotenuse?
An image in a quiz
√10 cm
Correct answer: √13
10 cm
13
Q3.
The right-angled triangle ABC has short sides of length 8 cm and 4 cm. Find the length of AC.
An image in a quiz
Correct answer: √80
12 cm
48 cm
80 cm
Q4.
Use Pythagoras’ Theorem to determine which of the sets of numbers below are Pythagorean triples:
2, 3, 4
Correct answer: 3, 4, 5
5, 6, 7
Q5.
Sandra tried to calculate the unknown length. What mistake has she made in Step 1?
An image in a quiz
Correct answer: She did not identify the hypotenuse correctly.
She did not need to square the numbers.
She should have written 6 + 10 = x squared.
Q6.
Sandra tried to calculate the unknown length. What mistake has she made in Step 2?
An image in a quiz
Made a mistake with re arranging the equation.
Mixed up the hypotenuse and shorter side lengths.
Correct answer: She doubled the sides instead of squaring.
Q7.
What do you need to do in order to find the area of the triangle shown below.
An image in a quiz
Find the length of the perpendicular height using Pythagoras then multiply by 32.
Find the length of the perpendicular height using Pythagoras then multiply by 68
Correct answer: Find the length of the perpendicular height using Pythagoras, multiply by 32 then divide by 2.
Multiply 32 x 68 then divide by 2.

6 Questions

Q1.
What is the coordinate of the point shown below?
An image in a quiz
(1, 2)
Correct answer: (2, 1)
2, 1
Q2.
The digram shows a right-angled triangle. Which of the statements is incorrect?
An image in a quiz
Correct answer: A
B
C
Q3.
Work out the length of the hypotenuse of the triangle shown below.
An image in a quiz
√77 cm
Correct answer: √85 cm
77 cm
85 cm
Q4.
Use Pythagoras’ Theorem to determine which of the sets of numbers below are Pythagorean triples:
5, 10, 15
Correct answer: 5, 12, 13
5, 8, 10
Q5.
What is the length of the line below
An image in a quiz
14
25
4
Correct answer: 5
Q6.
Find the distance between the points (2, 1) and (4, 3).
An image in a quiz
Correct answer: √8
2
4
8