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In the standard (x, y) coordinate plane, point A has coordinates (-4, -5). Point A is translated 4 units to the right and 5 units down. What are the coordinates of the image [tex]\( A' \)[/tex]?

A. (-9, -9)
B. (-8, -10)
C. (-4, -10)
D. (0, -10)
E. (8, 10)

Sagot :

GinnyAnsweridn
To solve this problem, let's go through it step by step.

1. Initial Coordinates of Point A:
Point [tex]\( A \)[/tex] has coordinates [tex]\((-4, -5)\)[/tex].

2. Translation Information:
- We need to translate the point 4 units to the right. Moving right means we add 4 to the x-coordinate.
- We also need to translate the point 5 units down. Moving down means we subtract 5 from the y-coordinate.

3. Calculate New Coordinates:
- For the x-coordinate: [tex]\( -4 + 4 \)[/tex]
- For the y-coordinate: [tex]\( -5 - 5 \)[/tex]

Let's compute these:
- New x-coordinate: [tex]\(-4 + 4 = 0\)[/tex]
- New y-coordinate: [tex]\(-5 - 5 = -10\)[/tex]

4. New Coordinates of Point [tex]\( A^{\prime} \)[/tex]:
After the translation, the new coordinates [tex]\( A^{\prime} \)[/tex] are [tex]\((0, -10)\)[/tex].

Thus, the coordinates of [tex]\( A^{\prime} \)[/tex] are [tex]\((0, -10)\)[/tex], which corresponds to option D.

Answer: [tex]\( D. (0, -10) \)[/tex]
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