Question

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

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

y = 1
2x + y = 2
x + y = 4
x + y = 1

Answer 1

Answer:

X+y=4

Step-by-step explanation:

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)

To map the square onto itself, it must be reflected over its diagonalThe diagonals of the square are: AC and BD. Using AC, we have:

A = (3,1)

(x1,y1)

C = (1,3)

(x2,y2)

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) + 1y = -x + 3 + 1y = -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.