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Translations — Quiz

Question 10 • Mathematics I

Square ABCD was translated using the rule open paren x comma y close paren rightarrow open paren x minus 4 comma y plus 15 close paren to form cap A prime cap b prime cap c prime cap d prime What are the coordinates of point cap d in the pre-image if the coordinates of point cap d prime in the image are open paren 9 comma negative 8 close paren ?

Answer
A
open paren negative 6 comma negative 4 close paren
B
open paren 5 comma 7 close paren
C
open paren 18 comma 1 close paren
D
open paren 13 comma negative 23 close paren

Explanation

The translation changes a pre-image point (x, y) to (x − 4, y + 15). To work backward from D′ = (9, −8), add 4 to the x-coordinate and subtract 15 from the y-coordinate: (9 + 4, −8 − 15) = (13, −23). Therefore, the pre-image coordinates are (13, −23), choice D.

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