Question

Polygon XYZ is translated 3 units to the left and 2 units up to create polygon X'Y'Z'. If point Y in polygon XYZ is located at coordinates (2, 7), where is point Y' in polygon X'Y'Z' located after the translation?

A) (5, 5)
B) (2, 7)
C) (5, 9)
D) (2, 9)

Answer 1

Point Y at (2, 7) would be translated to (-1, 9) after being moved 3 units to the left and 2 units up. There seems to be an error in the provided answer choices, as none of them correspond to the calculated coordinates.

Step-by-step explanation:

The student has asked where point Y' in polygon X'Y'Z' would be located after a translation of 3 units to the left and 2 units up from the original position of point Y at coordinates (2, 7). To answer this, we need to apply the translation to point Y's coordinates.

A translation in the Cartesian coordinate system involves shifting a point a certain number of units along the x-axis and the y-axis. Since we are moving 3 units to the left, we subtract 3 from the x-coordinate, and since we are moving 2 units up, we add 2 to the y-coordinate.

Subtraction of 3 units from the x-coordinate of point Y gives us:

x-coordinate: 2 - 3 = -1

Adding 2 units to the y-coordinate of point Y gives us:

y-coordinate: 7 + 2 = 9

Therefore, the new coordinates for point Y' are (-1, 9), which is not listed in the provided answer choices. There appears to be a mistake in the choices, as none of them match the calculated coordinates.