Question

If trapezoid JKLM is translated using the rule (x, y) → (x + 3, y − 3) and then translated using the rule (x, y) → (x − 1, y + 1) to create trapezoid J″K″L″M″, what is the location of L″?

Answer 1

After the initial translation of trapezoid JKLM by (3, -3), the coordinates of L become (6, -5). Then, after the second translation by (-1, 1), the final coordinates of L″ are (5, -4).

To find the location of L″ after the given translations, we need to apply each translation to the coordinates of L in the original trapezoid JKLM.

The first translation is (x, y) → (x + 3, y − 3). Applying this to L(3, -2):

L' = (3 + 3, -2 - 3) = (6, -5)

Now, L' becomes the new reference point for the second translation.

The second translation is (x, y) → (x − 1, y + 1). Applying this to L'(6, -5):

L'' = (6 - 1, -5 + 1) = (5, -4)

So, the location of L″ after the two translations is (5, -4).

Answer 2

L'' = (6, - 5 )

Explanation:

the translation rule (x, y ) → (x + 3, y - 3 ) means

add 3 to the original x- coordinate and

subtract 3 from the original y- coordinate

then

L (3, - 2 ) → L'' (3 + 3, - 2 - 3 ) → L'' (6, - 5 )