Triangle ABC has vertices A(5,6) , B(8,4) , and C(5,1) . The triangle is reflected around the x -axis and then around the y -axis to create triangle A′B′C′ . What is the x -coordinate of vertex B′ ?(1 point)

Question

Triangle ABC has vertices A(5,6) , B(8,4) , and C(5,1) . The triangle is reflected around the x -axis and then around the y -axis to create triangle A′B′C′ . What is the x -coordinate of vertex B′ ?(1 point)

Answer 1

First, let's reflect the triangle ABC across the x-axis.

When reflecting across the x-axis, the y-coordinate of each point will change sign.

So, the new coordinates of A(5,6) will be A'(5,-6), B(8,4) will be B'(8,-4), and C(5,1) will be C'(5,-1).

Now, reflect the triangle A'B'C' across the y-axis.

When reflecting across the y-axis, the x-coordinate of each point will change sign.

So, the final coordinates of A'(5,-6) will be A''(-5,-6), B'(8,-4) will be B''(-8,-4), and C'(5,-1) will be C''(-5,-1).

Therefore, the x-coordinate of vertex B'' is -8.

So, the x-coordinate of vertex B' is -8.