Question

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

Answer 1

When a shape is rotated, it must be rotated over a line.

The square must be reflected over line $x +y = 4$, for it to be mapped onto itself.

The points are given as:

$A = (3,1)$

$B = (3,3)$

$C = (1,3)$

$D = (1,1)$

To map the square onto itself, it must be reflected over its diagonal

The diagonals of the square are: AC and BD

Using AC, we have:

$A = (3,1)$ ---- $(x_1,y_1)$

$C = (1,3)$ ---- $(x_2,y_2)$

Start by calculating the slope (m)

$m = \frac{y_2 - y_1}{x_2 -x_1}$

So, we have:

$m = \frac{3-1}{1-3}$

$m = \frac{2}{-2}$

$m = -1$

The equation  is then calculated as:

$y = m(x - x_1) + y_1$

This gives:

$y = -1(x - 3) + 1$

$y = -x + 3 + 1$

$y = -x + 4$

Rewrite as:

$x +y = 4$

So, the square must be reflected over line $x +y = 4$, for it to be mapped onto itself.

See attachment for square ABCD and its line of reflection.

Read more about reflections at:

brainly.com/question/1878272