Question

Use the image to answer the question.

A grid shows a triangle A B C intersecting a vertical line at vertex B. Point D is plotted at the bottom of the vertical line below vertex B.

ΔABC
is the preimage of ΔA"B"C"
. To form ΔA"B"C"
, ΔABC
is reflected across line D
, then translated (x−2,y−4)
. How far is point C"
from point C
?

(1 point)
Responses

6 units
6 units

42–√ units
4 Start Root 2 End Root units

210 −−−√units
2 Start Root 10 End Root units

22–√ units
2 Start Root 2 End Root units
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Answer 1

4√2 units.

Reason: C is 3 units left of the vertical line. Reflection moves C 6 units to the right, then the translation (−2,−4) moves it 2 units left and 4 units down, so the net shift is (4,−4). Distance = sqrt(4^2+4^2) = sqrt(32) = 4√2.