What is the rule for finding the coordinates of an image reflected over the line y=-x?

The line y = - x is a lean line with an inclination of 45° measured clockwise from the negative x axis.

The reflection throunh this line would result in moving the x-coordinates to negative x and y-coordinates to negative y.

The rule is multiply each coordinate times negative 1.

We are given that the dimensions are 4 in x 9 in. To get the smallest possible square, first let us find for the LCM of 4 and 9.

4 = 0, 4, 8, 12, 16, 20, 24, 28, 32, 36

9 = 0, 9, 18, 27, 36

We can actually see that 36 is the least common multiple.

Therefore the smallest possible square has a dimension of:

36 inches by 36 inches