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A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?

A. [tex]\((x, y) \rightarrow (x+5, y-3)\)[/tex]
B. [tex]\((x, y) \rightarrow (x+5, y+3)\)[/tex]
C. [tex]\((x, y) \rightarrow (x-3, y+5)\)[/tex]
D. [tex]\((x, y) \rightarrow (x+3, y+5)\)[/tex]

Sagot :

GinnyAnsweridn
To determine the rule that describes the translation of a rectangle on a coordinate plane, we need to understand the effect of translating a point by a given number of units up or down and left or right.

Here is the step-by-step process:

1. Translation Up:
- Translating a point 5 units up means increasing the y-coordinate by 5. If a point is [tex]\((x, y)\)[/tex], after translating it 5 units up, the new position will be [tex]\((x, y + 5)\)[/tex].

2. Translation to the Left:
- Translating a point 3 units to the left means decreasing the x-coordinate by 3. If a point is [tex]\((x, y)\)[/tex], after translating it 3 units to the left, the new position will be [tex]\((x - 3, y)\)[/tex].

Combining these two effects, if we start with a point [tex]\((x, y)\)[/tex]:

- After moving 5 units up: The point becomes [tex]\((x, y + 5)\)[/tex].
- After then moving 3 units to the left: The point becomes [tex]\((x - 3, y + 5)\)[/tex].

Therefore, the rule that describes the translation of the rectangle 5 units up and 3 units to the left is:

[tex]\[ (x, y) \rightarrow (x - 3, y + 5) \][/tex]

Thus, the correct answer is:
[tex]\((x, y) \rightarrow (x - 3, y + 5)\)[/tex].
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