Question

Find the distance between the points
(i)(-7,-3) , (-5,-11)
(ii)(-6/5,3) , (-4,7/5)

Answer 1

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Answer 2

Answer:

The distance(D) formula is used to determine the distance between two points with the coordinates $(x_1 , y_1)$ and $(x_2, y_2)$ is;

D =$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

(i) (-7,-3) , (-5,-11)

To find the distance between them;

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

D = $\sqrt{(-5-(-7))^2+(-11-(-3))^2}$

or

D = $\sqrt{(-5+7)^2+(-11+3)^2}$ =$\sqrt{(2)^2+(-8)^2} = \sqrt{4+64} =\sqrt{68}$ $=4\sqrt{17}$

Therefore, the distance between the points  (-7,-3) and  (-5,-11) is, $4\sqrt{17}$

(ii) (-6/5,3) , (-4,7/5)

To find the distance between them;

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

D = $\sqrt{(-4-(\frac{-6}{5} ))^2+(\frac{7}{5} -3)^2}$

or

D = $\sqrt{(-4+\frac{6}{5} )^2+(\frac{7}{5}-3)^2}$ =$\sqrt{(\frac{-14}{5} )^2+(\frac{-8}{5} )^2} = \sqrt{\frac{196}{25} +\frac{64}{25} } =\sqrt{\frac{260}{25} }$

or

D =$4 \cdot\sqrt{\frac{13}{5}}$

Therefore, the distance between the points (-6/5,3) and (-4,7/5) is,

$4 \cdot\sqrt{\frac{13}{5}}$.