The distance between two points

4 The distance between two points

Referring again to the figure of HELM booklet 2, the distance between the points $A (x_{1}, y_{1})$ and $B (x_{2}, y_{2})$ is given using Pythagoras’ theorem by the following formula.

Key Point 10

Distance Between Two Points

The distance between points $A (x_{1}, y_{1})$ and $B (x_{2}, y_{2})$ is $\sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Task!

Find the distance between $A (- 7, 11)$ and $B (1, 3)$ , using Key Point 10.

$\sqrt{{(1 - (- 7))}^{2} + {(3 - 11)}^{2}} = \sqrt{64 + 64} = \sqrt{128}$

Exercises

Find the distance between the points $(4, 5)$ and $(- 17, 1)$ .
Find the distance between the points $(- 4, - 5)$ and $(1, 7)$ .

$\sqrt{457}$
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4 The distance between two points

Key Point 10

Task!

Answer

Exercises

Answer