Let T R2 R2 be a reflection in the line y x Find the image

Let

T: R² ? R²

be a reflection in the line

y = x.

Find the image of each vector

+ -6 points LarLinAlg7 6.5.003 Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector.

Solution

the reflection of a point (x, y) across a lline y =x is (y, x)

So,

a) (8,1) ---( 1, 8)

b) (-1, 0) ----(0, -1)

c) ( -a, 0) ----( 0, -a)

d) (0, -b) ---( -b , 0)

e) (c, -d) --- ( -d , c)

f) (-f , g) ---( g, -f)