Question

Given Triangle ABC with vertices A(3,2), B(5,5) and C(7.2). What are the coordinates of A' after being reflected over the line y=-x and then rotated 90 degrees counterclockwise? A' 6 5 B A 3 2 .c 9 -8 -7 -6 -5 -2 3 7 5 6 5 w -2 -3 4 -5 Your answer

Answer 1

For an arbitrary point (x,y), a reflection over the line y=-x is given by:

$(x,y)\rightarrow(-y,-x)$

The coordinates of the point A(3,2) after a reflection over the line y=-x, are:

$A^{\prime\prime}=(-2,-3)$

For an arbitrary point (x,y), a rotation of 90 degrees counterclockwise is given by:

$(x,y)\rightarrow(-y,x)$

The coordinates of the point A''(-2,-3) after rotating 90 degrees counterclockwise, are:

$A^{\prime}=(3,-2)$