Question

A segment with endpoints (5,8) and (-6,8) is rotated around the origin. How long will the new segment be?

Answer 1

The segment was only rotated, not changed. It would be the same length as the original.

To find the length, use the distance formula.

$\sqrt{ {(x2 - x1)}^{2} + ( {y2 - y1)}^{2} }$
(5, 8) would be point 1.

(-6,8) would be point 2.

Plug them into the formula.

$\sqrt{( { - 6 - 5)}^{2} + ( {8 - 8)}^{2} }$
Simplify.

$\sqrt{( { - 11)}^{2} + ( {0)}^{2} }$
$\sqrt{121 + 0}$
$\sqrt{121}$
Square root this answer.
$\sqrt{121} = + or - 11$
Negative distances aren't possible, so your answer is 11.

Hope this helped!

:)