Question

ma.912.gr.2.1

1. suppose δdef is the image of a translation of δabc. if point f is at (-2,6), write a rule for the translation that translates δabc to δdef.

a. (x,y) → (x + 3,y − 5)
b. (x,y) → (x − 3,y + 5)
c. (x,y) → (x + 1,y + 10)
d. (x,y) → (x − 5,y + 9)

Explanation:

Step1: Identify coordinates of point C

From the graph, point \( C \) is at \( (1, 1) \).

Step2: Determine translation from C to F

Point \( F \) is at \( (-2, 6) \). To find the translation rule, calculate the change in \( x \) and \( y \):

• Change in \( x \): \( -2 - 1 = -3 \) (so \( x \) becomes \( x - 3 \))
• Change in \( y \): \( 6 - 1 = 5 \) (so \( y \) becomes \( y + 5 \))

Thus, the translation rule is \( (x, y) \to (x - 3, y + 5) \), which matches option B.

Answer:

B. \( (x,y) \to (x - 3,y + 5) \)