Name the image of C after a rotation of 180° about the origin.

C'(-5, 2)

Step-by-step explanation:

Rule to be followed for a point rotated 180° about the origin,

(x, y) → (-x, -y)

From the figure attached,

When ABCD is rotated 180° about the origin, the new points of the image will be

A(2, 0) → A'(-2, 0)

B(4, 0) → B'(-4, 0)

C(5, -2) → C'(-5, 2)

D(1, -2) → D'(-1, 2)

Therefore, image of C will be C'(-5, 2).

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,