Question

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

(x, y) → (x + 5, y – 3)
(x, y) → (x + 5, y + 3)
(x, y) → (x – 3, y + 5)
(x, y) → (x + 3, y + 5)

Answer 1

Answer: Choice C

(x, y) → (x – 3, y + 5)

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Step-by-step explanation:

The "5 units up" portion means that each y value increases by 5. Therefore, we go from y to y+5. Going from x to x-3 means that we shift each point 3 units to the right.

For example, if the starting point is (1,7), then we have the following steps:

`(x,y) \to (x-3,y+5)\\\\(1,7) \to (1-3,7+5)\\\\(1,7) \to (-2,12)\\\\`

The point (1,7) moves 5 units up and 3 units to the left to arrive at (-2,12).

Note that the order doesn't matter. We could start moving 5 units up, then go 3 units left. Or we could start going 3 units left, then 5 units up. We'll arrive at the same destination.