Drag the three corners to reshape the triangle, then choose a mirror. The coordinates of the image change sign, but compare the side lengths in the third panel — not one of them moves.
Drag A, D or MThe faded triangle is the imageDashed lines join each point to its image
Mirror
(x, y) becomes (−x, y)
The original
A
(3, 4)
D
(7, 1)
M
(9, 6)
Reshape it however you like. Everything below updates as you drag.
The image
A′
(-3, 4)
D′
(-7, 1)
M′
(-9, 6)
Reflecting in the y-axis flips the sign of every x-coordinate and leaves y alone.
Side lengths
AD
5.00
A′D′
5.00
DM
5.39
D′M′
5.39
MA
6.32
M′A′
6.32
The two columns are always identical. A reflection moves a shape without stretching it, so distances survive untouched.
Noescio