Question

Find the distance between the pair of points left parenthesis 4 StartRoot 3 EndRoot comma StartRoot 7 EndRoot right parenthesis and left parenthesis negative StartRoot 3 EndRoot comma 5 StartRoot 7 EndRoot right parenthesis. If​ necessary, express the answer in simplified radical form and then round to two decimal places. The distance between the given points is nothing units. ​(Simplify your answer. Type an exact​ answer, using radicals as​ needed.) The distance between the given points is approximately nothing units.

Answer 1

Answer:

Exact distance:  $\sqrt{139}$ units.

Approximate distance: 11.8 units.

Step-by-step explanation:

We have been given two points $(4\sqrt{3},\sqrt{7})$ and $(\sqrt{3},5\sqrt{7})$. We are asked to find the distance between the given points.

We will use distance formula to solve our given problem.

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

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

$D=\sqrt{(3\sqrt{3})^2+(4\sqrt{7})^2}$

$D=\sqrt{9\cdot 3+16\cdot 7}$

$D=\sqrt{27+112}$

$D=\sqrt{139}$

Therefore, the distance between the given points is $\sqrt{139}$ units.

The approximate distance between the given points is $\sqrt{139}=11.7898\approx 11.8$ units.