Find the distances between the following pairs of points.
$(- 3, - 2)$ and $(- 6, 7)$ , the axes being inclined at $60^{o}$ .

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Solution

Distance between points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$
Then, distance between $A (- 3, - 2)$ and $B (- 6, 7)$ is
$A B = \sqrt{{(- 6 + 3)}^{2} + {(7 + 2)}^{2} + 2 (- 6 + 3) (7 + 2) cos 60^{\circ}} A B = \sqrt{9 + 81 - 27} A B = \sqrt{63} A B = 3 \sqrt{7}$

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Similar questions

(- 6, 7)

(- 1, - 5)

(- 2, - 3)

(3, 2)

60^{o}

x

y = 2 x + 5

2 y = (\sqrt{3} - 1) x + 7

A) (- 3, 45^{\circ}), (7, 105^{\circ})

B) (\sqrt{2}, \frac{π}{4}), (2, \frac{π}{2})

C) (3, \frac{π}{6}), (7, \frac{π}{6})

(2, 0)

(0, 3)

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