The relative distance or length remains unchanged.
Explanation:
Rotating an image does not change its dimensions, only its position within a coordinate system.
We can show this by rotating the line segment counter-clockwise about the origin through an angle π/2
A rotation of π /2 counter-clockwise maps:
( x , y ) → ( y , - x )
Using given points:
(3,7) → ( 7, -3 )
(–8,7) → (7,8)
Using the distance formula, with coordinates (3,7) and (–8,7)
[tex]d = \sqrt{(3 - (-8))^2 + (7-7)^2} = 11[/tex]
Using the distance formula, with coordinates (7,-3) and (7,8)
[tex]d = \sqrt{(7 - 7)^2 + ((-3) - 8)^2} = 11[/tex]
Therefore, the relative distance or length remains unchanged.
