Question

the translation above shows an object moving ________.
a. 6 units to the right and 6 units up
b. 6 units to the left and 6 units down
c. 7 units to the left and 7 units down
d. 7 units to the right and 7 units up

Explanation:

Pick a reference point on the original shape, e.g., the top-right corner at $(4, 3)$. Its corresponding point on the translated shape is $(-3, -3)$. Calculate the horizontal change: $-3 - 4 = -7$ (negative means left 7 units). Calculate the vertical change: $-3 - 3 = -6$? No, correct reference: take the top vertex of original shape at $(2,5)$. Translated vertex is $(-5,-1)$. Horizontal shift: $-5 - 2 = -7$ (7 left). Vertical shift: $-1 - 5 = -6$? No, recheck: original top vertex $(2,5)$, translated top vertex $(-5,-1)$: $-5-2=-7$ (left 7), $-1-5=-6$? No, wait the option B is 6 left 6 down, C is 7 left 7 down. Wait another point: original bottom of the "notch" at $(3,2)$. Translated point is $(-3,-4)$. $-3-3=-6$ (left 6), $-4-2=-6$ (down 6). Yes, this matches: 6 left, 6 down.

Answer:

B. 6 units to the left and 6 units down