Find the centre of rotation?

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1 Answer
Mar 5, 2018

The centre of rotation is #(–1, " "2).#

Explanation:

Figure #A# has been rotated 90° counter-clockwise to figure #B.# Pick one point on figure #A# and find its matching point in #B.#

I'll pick #P=(2,–2)# and its corresponding point #P^star=(3,5).#

Measure the vertical distance between these two points. Go from #B# to #A.#

My vertical distance is #5-(–2)=7#.

Measure the horizontal difference between them too, but this time, go from #A# to #B.#

My horizontal distance is #2-3=–1#.

Split the vertical difference #(7)# into the sum of two numbers that differ by the horizontal distance #(–1).#

My two numbers will be #3# and #4# in that order, since #3-4=–1.#

The centre of rotation will be #3# left and #4# up from our point in #A,# which puts it at

#color(white)= (2-3, "  "–2+4)#
#=(–1,"  "2)#.

We can see this is the centre of rotation because we can draw a #3xx4# rectangle with one corner at #(–1," "2)# and the other corner at either #P# or #P^star:#

From question above