Question

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1. parallelogram mnpq was translated 5 units to the right and 1 unit up to create parallelogram otpr. which rule describes the translation that was applied to the parallelogram?

a ((x,y)\to(x + 5,y + 1))
b ((x,y)\to(5x,y))
c ((x,y)\to(5 + x,1 + y))
d ((x,y)\to(x + 1,y + 5))

Explanation:

Step1: Recall translation rules

In coordinate geometry, translating a figure \( n \) units to the right means adding \( n \) to the \( x \)-coordinate, and translating \( m \) units up means adding \( m \) to the \( y \)-coordinate. The translation rule is \((x,y)\to(x + n,y + m)\) where \( n \) is the horizontal shift and \( m \) is the vertical shift.

Step2: Apply the given shifts

Here, the parallelogram is translated 5 units to the right (so \( n = 5 \)) and 1 unit up (so \( m = 1 \)). So the translation rule should be \((x,y)\to(x + 5,y + 1)\).

Looking at the options:

• Option A: \((x,y)\to(x + 5,y + 1)\) matches our derived rule.
• Option B: \((x,y)\to(5x,y)\) is a scaling in \( x \)-direction, not translation.
• Option C: \((x,y)\to(5 + x,1 + y)\) is the same as \((x,y)\to(x + 5,y + 1)\) (addition is commutative), but let's check the wording. Wait, no, the order of addition doesn't matter, but let's see the original shift. Wait, 5 units right is \( x+5 \), 1 unit up is \( y + 1 \). So \((x,y)\to(x + 5,y + 1)\) which is option A. Wait, option C is \((x,y)\to(5 + x,1 + y)\) which is equivalent, but maybe a typo? Wait, no, the problem says "5 units to the right and 1 unit up". So the correct rule is adding 5 to \( x \) and 1 to \( y \). So option A is \((x,y)\to(x + 5,y + 1)\) which is correct.

Answer:

A. \((x, y) \to (x + 5, y + 1)\)