Question

The vertices of polygon ABCD are at A(1,1), B(2,3), C(13,2), and D(12,1). ABCD is reflected across the x-axis and translated 2 units up to form polygon EFGH. Match each vertex of polygon EFGH to its coordinates. 1) (2, 1) 2) (1, 1) 3) (3, 0) 4) (2, 3) 5) (-3,4) (2, -1) 6) (-2,5)

Answer 1

To find the vertices of polygon EFGH, reflect the original vertices of polygon ABCD across the x-axis, then translate the reflected vertices up 2 units.

Step-by-step explanation:

To find the vertices of polygon EFGH, we will first reflect the original vertices of polygon ABCD across the x-axis. When we reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign. So, A(1,1) becomes A'(1,-1), B(2,3) becomes B'(2,-3), C(13,2) becomes C'(13,-2), and D(12,1) becomes D'(12,-1).

Next, we will translate the reflected vertices 2 units up. When we translate a point up, we add the same value to the y-coordinate. So, A'(1,-1) becomes E(1,-1+2), B'(2,-3) becomes F(2,-3+2), C'(13,-2) becomes G(13,-2+2), and D'(12,-1) becomes H(12,-1+2).

Therefore, the vertices of polygon EFGH are E(1,1), F(2,-1), G(13,0), and H(12,1). So, matching each vertex to its coordinates, we have 1) E(1,1), 2) F(2,-1), 3) G(13,0), and 4) H(12,1).

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