Trapezoid JKLM is shown on the coordinate plane.
Trapezoid JKLM on the coordinate plane with ordered pairs at J negative 2, 1, at K 1, 1, at L 3, negative 2, at M negative 4, negative 2.
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 − 2) to create trapezoid J″K″L″M″, what is the location of L″?
(−4, 5)
(2, −4)
(7, −7)
(9, −6)
To find the new location of point L″ after the two translations, we first apply the translation (x, y) → (x + 3, y − 3) to point L(3, -2).
Applying the first translation:
L′(3 + 3, -2 - 3) = L′(6, -5)
Now, we apply the second translation (x, y) → (x + 1, y − 2) to point L′(6, -5).
Applying the second translation:
L″(6 + 1, -5 - 2) = L″(7, -7)
Therefore, the location of point L″ is (7, -7). So, the correct answer is:
(7, −7).