The trace of a matrix is given by the sum of its diagonal entries. in general, the trace of a matrix is equal to the sum of its eigenvalues, and its determinant is equal to the product of its eigenvalues. verify this for 2 × 2 matrices.

Given:

A(-8,7) → A'(-7-8)

B(-4,7) → B'(-7,-4)

C(-6,2) → C'(-2,-6)

To find:

The transformation occurred between the set of points above.

Solution:

From the given set of points it is clear that the rule of transformation is

(x,y) → (-y,x)            ...(i)

Because in the given set of points we interchange the x and y coordinates, then we are applying negative sign in the x-coordinate.

If a figure reflection over the x-axis, then

(x,y) → (x,-y)

If a figure reflection over the y-axis, then

(x,y) → (-x,y)

If a figure rotated 90° clockwise, then

(x,y) → (y,-x)

If a figure rotated 90° counterclockwise, then

(x,y) → (-y,x)

Only this rule of transformation is same as (i). So, the figure is rotated 90° counterclockwise.

Therefore, the correct option is D.