Which of the following would be a line of reflection that would map ABC D onto itself

D) -3x + 3y = 9

Step-by-step explanation:

Any line that cuts the figure in two equal halves will be a solution of this problem.

For example, the lines y = 1 and x = -2 cut the square in two equal halfves.

Now, the other two lines that cut the square in two equal halfves are the lines:

AC and BD.

Let's find the equations for these lines:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

The line AC is:

A = (-3, 0) C = (-1, 2)

The slope of this line is:

a = (2 - 0)/(-1 - (-3)) = 1

y = 1*x + b

And when x = -1, we have that y = 2.

Then:

2 = 1*-1 + b

2 + 1 = b

Then the line AB is:

y = 1*x + 3.

Now, if we multiply both parts of the equation by the same number, the line does not change.

Multiply both sides by 3:

3*y = 3*x + 9.

Let's put our two variables on the left side and get:

-3x + 3y = 9

This is option D, then D is a correct option.

Now let's analyze the line BD.

B = (-3, 2) and D = (-1, 0)

The slope is:

a = (0 - 2)/(-1 - (-3) = -1

y = -1*x + b

And we know that when x = -1, y = 0 then:

0 = -1*-1 + b

1 = b

Then this line is:

y = -1*x + 1.

This line does not fit with any of the given options.

Then the only correct option is:

D) -3x + 3y = 9.

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