[Math] How to find the rectangle center point (origin position)

Question

If I have a rectangle and I try to rotate it, how to find the rectangle center point (origin position)?
I know these $3$ corners of the rectangle:

• left top: $(0,5)$
• left bottom: $(0,0)$
• right top: $(5,5)$

Answer 1

Use the fact that the centre $(h,k)$ of a rectangle is the midpoint of the diagonals:

$h=\frac{0+5}2, k=\frac{5+0}2 $

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Alternatively, use the fact the centre $(h,k)$ of a rectangle is equidistant from the corners, so that $$(h-0)^2+(k-0)^2=(h-0)^2+(k-5)^2=(h-5)^2+(k-5)^2$$

Use the 1st two to get $h$ and the last two to get $k.$