Question

4) Find the distance between the points R (0, -3), S (0, 5/3


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Answer 1

Answer:

distance between S and R = 4.67 units

Answer 2

Answer:

The distance between the given points is 4.67 units approximately.

Step-by-step-explanation:

The coordinates of the given points are

$\displaystyle{\sf\:R\:\equiv\:(\;0\;-\;3\;)\:\equiv\:(\;x_1\;,\;y_1\;)}$

$\displaystyle{\sf\:S\:\equiv\:\left(\:0\:,\:\dfrac{5}{3}\:\right)\:\equiv\:(\:x_2\:,\:y_2\:)}$

We have to find the distance between these two points.

We know that,

$\displaystyle{\pink{\sf\:d\:(\;R\;,\;S\;)\:=\:\sqrt{(\;x_1\;-\;x_2\;)^2\:+\:(\;y_1\;-\;y_2\;)^2\:}}}$

$\displaystyle{\implies\sf\:d\:(\;R\;,\;S\;)\:=\:\sqrt{(\;0\;-\;0\;)^2\:+\:\left(\;-\;3\;-\;\dfrac{5}{3}\;\right)^2}}$

$\displaystyle{\implies\sf\:d\:(\;R\;,\;S\;)\:=\:\sqrt{(\;0\;)^2\:+\:\left(\:\dfrac{-\;9\;-\;5}{3}\;\right)^2}}$

$\displaystyle{\implies\sf\:d\:(\;R\;,\;S\;)\:=\:\sqrt{0\:+\:\left(\:\dfrac{-\:14}{3}\:\right)^2}}$

$\displaystyle{\implies\sf\:d\:(\;R\;,\;S\;)\:=\:\sqrt{\dfrac{-\:14\:\times\:-\:14}{3\:\times\:3}}}$

$\displaystyle{\implies\sf\:d\:(\;R\;,\;S\;)\:=\:\sqrt{\dfrac{196}{9}}}$

$\displaystyle{\implies\sf\:d\:(\;R\;,\;S\;)\:=\:\cancel{\dfrac{14}{3}}}$

$\displaystyle{\implies\sf\:d\:(\;R\;,\;S\;)\:=\:4.666}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:d\:(\;R\;,\;S\;)\:\approx\:4.67\:units\:}}}}$

∴ The distance between the given points is 4.67 units approximately.