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10.02 Distance and the Pythagorean theorem

Adaptive
Worksheet

Interactive practice questions

Consider the triangle shown below.

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a

Complete the steps which calculate the length $AC$AC:

$AC^2=AB^2+BC^2$AC2=AB2+BC2

$AC^2=$AC2=$\left(\editable{}\right)^2+\left(\editable{}\right)^2$()2+()2

$AC^2=$AC2=$\editable{}+\editable{}$+

$AC^2=$AC2=$\editable{}$

b

Hence find the exact length of $AC$AC.

Easy
1min

Use the triangle and Pythagoras' theorem to complete the following:

Easy
2min

The points $P$P $\left(-6,5\right)$(6,5), $Q$Q $\left(-6,2\right)$(6,2) and $R$R $\left(-2,2\right)$(2,2) are the vertices of a right triangle, as shown on the number plane.

Medium
2min

The points $P$P $\left(-1,9\right)$(1,9), $Q$Q $\left(-1,6\right)$(1,6) and $R$R $\left(-5,6\right)$(5,6) are the vertices of a right triangle, as shown on the number plane.

Medium
1min
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Outcomes

M1.N.Q.A.1.A

Choose and interpret the scale and the origin in graphs and data displays.*

M1.G.GPE.A.3

Understand the relationship between the Pythagorean Theorem and the distance formula and use an efficient method to solve problems on the coordinate plane.

M1.MP1

Make sense of problems and persevere in solving them.

M1.MP2

Reason abstractly and quantitatively.

M1.MP3

Construct viable arguments and critique the reasoning of others.

M1.MP4

Model with mathematics.

M1.MP5

Use appropriate tools strategically.

M1.MP6

Attend to precision.

M1.MP7

Look for and make use of structure.

M1.MP8

Look for and express regularity in repeated reasoning.

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