Question

Graph XY with endpoints X(-3, 1) and Y(4,-5) and its image after the composition.

Rotation: 180° about the origin
Translation: (x, y)→(x − 1, y + 1)
Segment
di
-4
Undo
-2
6
4
2
0
-2
Redo
x Reset

Answer 1

To graph the line segment XY with endpoints X(-3, 1) and Y(4, -5), plot the points and apply the rotation and translation.

Step-by-step explanation:

To graph the line segment XY with endpoints X(-3, 1) and Y(4, -5), we plot the points X and Y on a coordinate plane.

X(-3, 1) is located 3 units to the left of the origin and 1 unit above the origin. Y(4, -5) is located 4 units to the right of the origin and 5 units below the origin.

After rotating the graph 180° about the origin, the points X and Y will switch their positions. X will now be located at (3, -1), and Y will be located at (-4, 5).

Then, after translating the graph by subtracting 1 from the x-coordinate and adding 1 to the y-coordinate, the points X and Y will shift to (2, 0) and (-5, 6) respectively.

The resulting line segment after the composition of rotation and translation is the segment connecting the points (2, 0) and (-5, 6).

Learn more about Graphing a line segment and applying rotation and translation