Question

Suppose ADEF is the image of a translation of AABC. If D is at (-6, -2), what translation rule maps 4ABC to ADEF?

Answer 1

To find the translation rule that maps triangle ABC to triangle DEF, one must calculate the horizontal and vertical shifts using the coordinates of corresponding points in both triangles.

The question involves determining the translation rule that maps triangle ABC to its image, triangle DEF, in a geometric transformation. Since D is given as (-6, -2), we'll need the coordinates of the corresponding point in triangle ABC to find the translation rule. Once we know the coordinates of both corresponding points, we can find the change in x (horizontal shift) and y (vertical shift) to define the translation rule.

For instance, if point A in triangle ABC has coordinates (x1, y1) and its image, point D, in triangle DEF has coordinates (x2, y2), then the translation rule can be described as (x2 - x1, y2 - y1). This rule tells us how much to move every point in triangle ABC horizontally and vertically to obtain triangle DEF.

Completed Version:

Suppose ADEF is the image of a translation of AABC. If D is at (-6, -2), what translation rule maps 4ABC to ADEF?

a) T(9,2) (ΔABC) = ΔDEF

b) T(9,-2) (ΔABC) = ΔDEF

c) T(-9,2) (ΔABC) = ΔDEF

d) T(-9,-2) (ΔABC) = ΔDEF

Answer 2

Answer: D. T <-9, -2> (ΔABC) = ΔDEF

Explanation:

D = A

A (3, 0) --> D (-6, -2)

To get the x-coordinate of D, you add -9 to 3

To get the y-coordinate of D, you add -2 to 0

T <-9, -2> (ΔABC) = ΔDEF

Hope this helped!