Question

The vertices of polygon ABCD are at A(1,1), B(2,3), C(3,2), and D(2,1). ABCD is reflected across the x-axis and translated 2 units up to form polygon A' B'C'D' to it's coordinates.

Answer 1

The coordinates of the polygon A'B'C'D' following a reflection across the x-axis and a translation 2 units up are;

• A'(1, 1), B'(2, -1), C'(3, 0), and D'(2, 1)

How can the coordinates of the image be found?

The vertices of the polygon are;

A(1, 1), B(2, 3), C(3, 2), and D(2, 1)

Reflection over the x-axis gives;

(x, y) reflection across the x-axis → (x, -y)

Which gives;

A(1, 1) R x-axis → A''(1, -1)

B(2, 3) R x-axis → B''(2, -3)

C(3, 2) R x-axis → C''(3, -2)

D(2, 1) R x-axis → D''(2, -1)

Translation of the points ABCD 2 units up gives;

A''(1, -1) T(0, 2) → A'(1, -1 + 2) = A'(1, 1)

B''(2, -3) T(0, 2) → B'(2, -3 + 2) = B'(2, -1)

C''(3, -2) T(0, 2) → C'(3, -2 + 2) = C'(3, 0)

D''(2, -1) T(0, 2) → D'(2, -1 + 2) = D'(2, 1)

The coordinates of A'B'C'D' are therefore;

• A'(1, 1), B'(2, -1), C'(3, 0), and D'(2, 1)

Learn more about reflection and translation transformations here:

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