Question

Draw a polygon with vertices A(6, 7) , B(8, 4) , C(5, 2) , and D(2, 3) . Then draw its image after a translation by the vector ⟨−4,−2⟩ . Write the coordinate rule for the translation.

Answer 1

To draw the image of the given polygon after a translation by the vector ⟨−4,−2⟩, subtract the x-component of the vector from the x-coordinate of each vertex and subtract the y-component of the vector from the y-coordinate of each vertex. The image coordinates for the given vertices are A'(2, 5), B'(4, 2), C'(1, 0), and D'(-2, 1). The coordinate rule for the translation is (x, y) → (x-4, y-2).

Step-by-step explanation:

To draw the image of the polygon after a translation by the vector ⟨−4,−2⟩, we need to subtract the x-component of the vector from the x-coordinate of each vertex, and subtract the y-component of the vector from the y-coordinate of each vertex. To draw the image of the given polygon after a translation by the vector ⟨−4,−2⟩, subtract the x-component of the vector from the x-coordinate of each vertex and subtract the y-component of the vector from the y-coordinate of each vertex.

The image coordinates for the given vertices are A'(2, 5), B'(4, 2), C'(1, 0), and D'(-2, 1). The coordinate rule for the translation is (x, y) → (x-4, y-2).

The image of vertex A would be A'(-4+6, -2+7) = A'(2, 5), the image of vertex B would be B'(-4+8, -2+4) = B'(4, 2), the image of vertex C would be C'(-4+5, -2+2) = C'(1, 0), and the image of vertex D would be D'(-4+2, -2+3) = D'(-2, 1).

The coordinate rule for the translation is (x, y) → (x-4, y-2).