Question

Which of the following would be a line of reflection that would map ABCD onto itself?

Square ABCD with A at negative 3 comma 0, B at negative 3 comma 2, C at negative 1 comma 2, and D at negative 1 comma 0.

A. y = 2
B. 3x + y = 1
C. 3x + y = −1
D. −3x + 3y = 9

Answer 1

D. -3x +3y = 9

Step-by-step explanation:

You want the line of reflection that maps square ABCD to itself. Its vertices are A(-3, 0), B(-3, 2), C(-1, 2), D(-1, 0).

Square

The given points lie on the lines x=-3, y=2, x=-1, y=0. Its midpoint is ...

(x, y) = (-3-1, 2+0)/2 = (-4, 2)/2 = (-2, 1)

Since the square is aligned with the grid, its lines of reflection are any of ...

• a horizontal line through the midpoint, y = 1
• a vertical line through the midpoint, x = -2
• a diagonal line with a slope of 1 through the midpoint
• a diagonal line with a slope of -1 through the midpoint

Lines

In point-slope form, the equations of the diagonal lines are ...

y -1 = 1(x +2) . . . . . line with slope 1 through midpoint (-2, 1)

y = x +3

-3x +3y = 9 . . . . . . . in the form matching answer choice D

And the other diagonal line is ...

y -1 = -1(x +2)

y = -x -1

3x +3y = -3 . . . . . . in a form with x-coefficient 3 (matches no choice)

The attachment shows the square and the line of reflection that maps it to itself. (Other answer choices are shown in light gray.)