can you please help me with this

Question

The coordinates of a triangle are (2, 5), (5, 9), and (8, 11). The coordinates of the image of the triangle after it is translated are (–1, 3), (2, 7), and (5, 9). Which best describes the triangle’s translation?

1. a. down 2 units and right 3 units.
2. c. down 2 units and left 3 units.
3. d. down 3 units and left 2 units.

Answer 1

So when we're looking at the image of a point, the change in the x coordinate will tell us how far we're shifting right (+) or left (-) and the change in the y coordinate will tell us how far we're shifting up (+) or down (-).

Assuming the set of points of the image are listed in the order of their pre-images, then let's look at the difference between the coordinates of each point respectively:

(2, 5) --> (x - 3, y - 2) --> (-1, 3)

(5, 9) --> (x - 3, y - 2) --> (2, 7)

(8, 11) --> (x - 3, y - 2) --> (5, 9)

Each x coordinate can be subtracted by 3 and each y coordinate can be subtracted by 2 to obtain the image.

Thus, the triangle is translated down 2 units and left 3 units, answer choice C.

Answer 2

Hi...

Not sure why there is NO (b) choice among the answers but no matter.

Comparing the coordinates of the PREIMAGE (original triangle) to the NEW coordinates after translation

A (2, 5). B (5, 9), C (8, 11)

A' (-1, 3), B' (2, 7), C' (5, 9)

Note that all x coordinates have DECREASED by 3 and y coordinates have DECREASED by 2.

DECREASED in the x-axis means the points have moved LEFT.

(2 to -1), (5 to 2) and (8 to 5)

DECREASED in the y-axis means the points have moved DOWN.

(5 to 3), (9 to 7) and (11 to 9)

Graph the points so you can see the translation.

So the answer is (c)

Hope this helps.