This question says "The vertices of triangle ABC are A(-1,1), B(0,3), and C(3,4). Graph the image of triangle ABC after a compositon of the following transformations in the order they were listed. Translation: (x,y) translates to (x-3, y-3) Reflection: in the line y=x

I understand how to do the translation but not the reflection.Thanks in advance!

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The vertices of triangle ABC are A(-1,1), B(0,3), and C(3,4). Reflection: in the line y=x

We need to find point A'(x,y) such that AA' the distance between A and A',perpendicularly bisected by line y=x.

Let AA' meets y=x at M ie. AM is perpendicular to y=x

Find equation of line AM, slope of AM is -1 (perpendicular to y=x ,its slope is 1) and posses through (-1,1)

y-1=-1(x+1)

y-1=-x-1

y=-x (i)

y= x (ii) (given line)

find point of intersection of (i) and (ii) i.e (0,0),By mid point formula

(x-1)/2=0 , (y+1)/2=0

x=1 and y=-1

Thus coordinate of A'(1,-1)

Thus reflection of A(-1,1) with respect to line y=x is A'(1,-1).

similarly you can find B' and C'.

Sorry I forget ,

Thus reflection of B(0,3) with respect to line y=x is B'(3,0).

and reflection of C(3,4) with respect to line y=x is C'(4,3).

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