Question

Polygon ABCDEF is reflected across the line y=−x
, translated up 3 units and to the left 2 units, and then rotated 90°
counterclockwise to produce the image polygon A'B'C'D'E'F'.

What are the coordinates of D'?

Answer 1

To find the coordinates of D', we need to first reflect polygon ABCDEF across the line y = -x, then translate the reflected polygon up 3 units and to the left 2 units, and finally rotate it 90° counterclockwise.

1. Reflection across y = -x:
The reflection across the line y = -x is equivalent to interchanging the x and y coordinates of each point. So, for point D(4, 3), after reflecting we have D' : (3, 4).

2. Translation up 3 units and left 2 units:
After translating D' three units up and two units to the left, we get the new coordinates of D':
D' : (3 - 2, 4 + 3) = D' : (1, 7).

Therefore, the coordinates of D' are (1, 7).