Question

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1. what is the rule that maps ( \triangle hij ) onto ( \triangle h^{prime}i^{prime}j^{prime} )?

a. ( (x, y)
ightarrow(x+2, y+4) )
b. ( (x, y)
ightarrow(x-2, y-4) )
c. ( (x, y)
ightarrow(x+4, y+2) )
d. ( (x, y)
ightarrow(x-4, y-2) )

Explanation:

Step1: Find the change in \(x\)-coordinates

Let's take a point from \(\triangle HIJ\) and its corresponding point in \(\triangle H'I'J'\). For example, take \(H(-3,3)\) and \(H'(1,7)\).
The change in \(x\)-coordinate: \(1-(-3)=1 + 3=4\).

Step2: Find the change in \(y\)-coordinates

For the same points \(H(-3,3)\) and \(H'(1,7)\).
The change in \(y\)-coordinate: \(7 - 3=4\).
Let's check another point. Take \(I(-5,1)\) and \(I'(-1,5)\).
Change in \(x\): \(-1-(-5)=-1 + 5 = 4\).
Change in \(y\): \(5 - 1=4\).

Answer:

C. \((x,y)\to(x + 4,y+4)\)