Question

Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane. Original coordinates of vertices: (-8, -4), (-6, 1), (-6, -2), (-8, -2). Shift: six units up, four units to the right

Answer 1

To determine the new coordinates of the polygon's vertices after a translation, add the shift values to the original x and y coordinates of each vertex. The new vertices' coordinates are (-4, 2), (-2, 7), (-2, 4), and (-4, 4).

Step-by-step explanation:

To find the new coordinates of the vertices after the translation, we need to add the shift to the original coordinates. The shift is six units up (positive on the y-axis) and four units to the right (positive on the x-axis).

• For the first vertex (-8, -4), the new coordinates will be (-8 + 4, -4 + 6) = (-4, 2).
• For the second vertex (-6, 1), the new coordinates will be (-6 + 4, 1 + 6) = (-2, 7).
• For the third vertex (-6, -2), the new coordinates will be (-6 + 4, -2 + 6) = (-2, 4).
• For the fourth vertex (-8, -2), the new coordinates will be (-8 + 4, -2 + 6) = (-4, 4).

The new coordinates of the vertices after the translation are:

• Vertex A: (-4, 2)
• Vertex B: (-2, 7)
• Vertex C: (-2, 4)
• Vertex D: (-4, 4)