Find the exact distance between the points.
-$( \sqrt { 5 } , - \sqrt { 3 } )$ and $( 4 \sqrt { 5 } , - 7 \sqrt { 3 } )$
A) $3 \sqrt { 17 }$
B) $6 \sqrt { 7 }$
C) $2 \sqrt { 42 }$
D) $2 \sqrt { 58 }$

Question

Quizplus · Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Applying this formula to the given points $(\sqrt{5}, -\sqrt{3})$ and $(4\sqrt{5}, -7\sqrt{3})$, we get $\sqrt{(4\sqrt{5} - \sqrt{5})^2 + (-7\sqrt{3} + \sqrt{3})^2} = \sqrt{(3\sqrt{5})^2 + (-6\sqrt{3})^2} = \sqrt{45 + 108} = \sqrt{153} = 3\sqrt{17}$.

Find the Exact Distance Between the Points (5,−3)( \sqrt { 5 } , - \sqrt { 3 } )(5​,−3​)

Find the Exact Distance Between the Points $( \sqrt { 5 } , - \sqrt { 3 } )$