Which is a rule that describes the translation of a point form (4, –8) to (7, –10)?
A. (x, y) arrow(x + 3, y – 2)
B. (x, y) arrow(x + 3, y + 2)
C. (x, y) arrow(x – 3, y – 2)
D. (x, y) arrow(x – 3, y + 2)
A. (x, y) arrow(x + 3, y – 2)
To determine the rule that describes the translation of a point from (4, -8) to (7, -10), we need to analyze the change in the x-coordinate and the change in the y-coordinate.
First, let's consider the change in the x-coordinate. The x-coordinate of the initial point is 4, and the x-coordinate of the final point is 7. Therefore, the change in the x-coordinate is 7 - 4 = 3.
Next, let's consider the change in the y-coordinate. The y-coordinate of the initial point is -8, and the y-coordinate of the final point is -10. Therefore, the change in the y-coordinate is -10 - (-8) = -10 + 8 = -2.
Now, we can write down the rule. The rule for translating the point (4, -8) to (7, -10) is:
(x, y) → (x + 3, y - 2)
Based on the given answer choices, the correct option that matches this rule is:
A. (x, y) arrow(x + 3, y - 2)
To describe the translation of a point from (4, -8) to (7, -10), we can observe the change in coordinates.
The x-coordinate increased by 3 units, and the y-coordinate decreased by 2 units.
So, the rule that describes this translation is: (x, y) arrow (x + 3, y - 2).
Therefore, the correct answer is A. (x, y) arrow (x + 3, y - 2).