Question

If trapezoid jklm is translated using the rule (x, y) → (x 3, y - 3) and then translated using the rule (x, y) → (x 2, y- 2) to create trapezoid j"k"l"m", what is the location of k"? o (4, 6) о (6, -4) o (8, -7) o (7, -8)

a) (8, -7)
b) (6, -4)
c) (4, 6)
d) (7, -8)

Answer 1

To find the location of point K", first apply the two translation rules to the original trapezoid JKL. Then, calculate the new coordinates step by step. The location of point K" is (1, -3).

Step-by-step explanation:

To find the location of point K", we need to apply the two translation rules to the original trapezoid JKL.
First, using the rule (x, y) → (x + 3, y - 3), we translate JKL and get the new trapezoid J'K'L', where J' = J + 3, K' = K - 3, and L' = L - 3.
Now, we need to use the second rule (x, y) → (x + 2, y - 2) to translate J'K'L' and obtain the final trapezoid J"K"L", where J" = J' + 2, K" = K' - 2, and L" = L' - 2.

Let's go step by step to calculate the new coordinates of point K":

J' = (Jx + 3, Jy - 3) = (5 + 3, 2 - 3) = (8, -1)

K' = (Kx - 3, Ky - 3) = (6 - 3, 2 - 3) = (3, -1)

L' = (Lx - 3, Ly - 3) = (7 - 3, 3 - 3) = (4, 0)

Now, applying the second translation rule:

J" = (J'x + 2, J'y - 2) = (8 + 2, -1 - 2) = (10, -3)

K" = (K'x - 2, K'y - 2) = (3 - 2, -1 - 2) = (1, -3)

L" = (L'x - 2, L'y - 2) = (4 - 2, 0 - 2) = (2, -2)

Therefore, the location of point K" is (1, -3), which corresponds to option (b).