Question

A translation maps the point (-5, -1) to the point (4, 2). Describe the translation and find the image of (4, -1) under the same translation.

a) The translation is right by 9 units and up by 3 units. The image of (4, -1) is (13, 2).
b) The translation is left by 9 units and down by 3 units. The image of (4, -1) is (-5, -4).
c) The translation is right by 9 units and up by 3 units. The image of (4, -1) is (9, 2).
d) The translation is left by 9 units and down by 3 units. The image of (4, -1) is (13, -4).

Answer 1

A translation maps a point in one location to a new location by adding or subtracting values from the coordinates. The translation for (-5, -1) to (4, 2) is right by 9 units and up by 3 units. The image of (4, -1) under the same translation is (13, 2).

Step-by-step explanation:

A translation maps a point in one location to a new location. In this case, the translation maps the point (-5, -1) to the point (4, 2).

To find the translation, we subtract the x-coordinate of the initial point from the x-coordinate of the final point, and we subtract the y-coordinate of the initial point from the y-coordinate of the final point. Therefore, the translation is right by 9 units and up by 3 units.

To find the image of (4, -1) under the same translation, we apply the same translation vector to the point (4, -1). Adding 9 to the x-coordinate will give the new x-coordinate, and adding 3 to the y-coordinate will give the new y-coordinate. Therefore, the image of (4, -1) is (13, 2).