Question

Figure ABCD is reflected across the x-axis.

Answer 1

Reflection across the x-axis will move every point down to a distance that is twice their y-coordinates.

So, A (2, 3) will be moved to A'(2, 3-6) = A'(2, -3).

B (5, 5) will be moved to B'(5, 5-10) = B'(5, -5).

C (7, 3) will be moved to C'(7, 3-6) = C'(7, -3) and

D (5, 2) will be moved to D'(5, 2-4) = D'(5, -2).

Answer 2

Answer: The required vertices after reflection are A'(2, -3), B'(5, -5), C'(7, -3) and D'(5, -2).

Step-by-step explanation:  Given that the figure ABCD is reflected across the X-axis.

We are to find the co-ordinates of A, B, C and D after reflection.

From the figure, we note that the co-ordinates of the vertices of ABCD are

A(2, 3), B(5, 5), C(7, 3) and D(5, 2).

After reflection from X-axis, the y co-ordinate of each vertex will change its sign (y → -y).

Therefore,  the vertices of ABCD after reflection are

A(2, 3)  ⇒ A'(2, -3),

B(5, 5)  ⇒  B'(5, -5),

C(7, 3)  ⇒  C'(7, -3),

D(5, 2)  ⇒ D'(5, -2).

Thus, the required vertices after reflection are A'(2, -3), B'(5, -5), C'(7, -3) and D'(5, -2).