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A triangle is translated by using the rule [tex]\((x, y) \rightarrow (x-4, y+1)\)[/tex]. Which describes how the figure is moved?

A. Four units left and one unit down
B. Four units left and one unit up
C. One unit right and four units down
D. One unit right and four units up

Sagot :

GinnyAnsweridn
To determine how the triangle is moved, we analyze the translation rule given: [tex]\((x, y) \rightarrow (x-4, y+1)\)[/tex].

1. Horizontal Movement:
- The translation rule shows that [tex]\(x\)[/tex] is replaced by [tex]\(x-4\)[/tex].
- Subtracting 4 from [tex]\(x\)[/tex] means that for every point on the triangle, the x-coordinate decreases by 4.
- A decrease in the x-coordinate by 4 units means the figure is moved 4 units to the left.

2. Vertical Movement:
- The translation rule shows that [tex]\(y\)[/tex] is replaced by [tex]\(y+1\)[/tex].
- Adding 1 to [tex]\(y\)[/tex] means that for every point on the triangle, the y-coordinate increases by 1.
- An increase in the y-coordinate by 1 unit means the figure is moved 1 unit up.

Therefore, the triangle is translated 4 units to the left and 1 unit up.

So, the option that correctly describes how the figure is moved is:
four units left and one unit up.
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