Question

What is the image of A(3, -1) after a reflection, first across the line y = 3, and then across the line x = -1?(-5, 7)(1,-5)(-5, -1)(3,-1)

Answer 1

(-5, 7)

Step-by-step explanation

We want to reflect A(3, -1)

ACROSS y = 3

Because it is a reflection across a horizontal line, we will only deal with the y coordinate.

We have to find the distance of the y coordinate from the point y = 3.

The y coordinate of A is -1, so the distance is:

3 -(-1) = 3 + 1

= 4

Now, add that value to 3 (from y = 3). That is:

3 + 4 = 7

This is the new y coordinate of A.

A becomes:

A(3, 7)

ACROSS x = -1

Because it s a reflection across a vertical line, we will deal only with the x coordinate.

We have to find the distance of the x coordinate from the point x = -1.

The x coordinate of A is 3, so the distance is:

-1 - 3 = -4

Now, add that value to -1 (from x = -1). That is:

-4 - 1 = -5

This is the new x coordinate of A.

A becomes:

A(-5, 7)

Therefore, after the two reflections, the coordinate of the image of A is A(-5, 7)