Question

select the correct answer.
figure 1 has been transformed to produce figure 2.
which notation describes this transformation?
a. ((x, y) = (x + 9, y - 2))
b. ((x, y) = (-y, x))
c. ((x, y) = (x - 9, y + 2))
d. ((x, y) = (-x, y))

Explanation:

Step1: Analyze transformation type

Figure 1 (red) to Figure 2 (pink) seems a translation? Wait, no, check coordinates. Let's pick a vertex of Figure 1, say a point. Let's take a vertex of Figure 1: suppose one vertex is (3, -5) (approx), and Figure 2 has a vertex at (-6, -3)? Wait, no, better to check the translation. Wait, let's see the x and y changes. Let's take a corresponding point. Let's say a vertex of Figure 1: let's find coordinates. Figure 1: let's take the rightmost point, maybe (7, -5)? Figure 2: leftmost point (-6, -3)? Wait, no, maybe better to calculate the translation. Let's take a point from Figure 1: let's say (x, y) and Figure 2: (x', y'). Let's pick a vertex. Let's say Figure 1 has a vertex at (3, -5), Figure 2 has a vertex at (-6, -3). Wait, x changes from 3 to -6: 3 - 9 = -6. y changes from -5 to -3: -5 + 2 = -3. So (x', y') = (x - 9, y + 2). Wait, but option C is (x', y') = (x - 9, y + 2). Wait, but let's check another point. Let's take the top vertex of Figure 1: maybe (5, -4), Figure 2: (-4, -2). 5 - 9 = -4, -4 + 2 = -2. Yes! So the translation is x decreases by 9 (x - 9) and y increases by 2 (y + 2). So the notation is (x', y') = (x - 9, y + 2), which is option C? Wait, no, wait the options: A: (x+9, y-2), B: (-y, x), C: (x-9, y+2), D: (-x, y). Wait, let's recheck. Wait, Figure 1 is on the right, Figure 2 on the left. So moving left 9 units (x - 9) and up 2 units (y + 2). So yes, (x', y') = (x - 9, y + 2), which is option C. Wait, but let's confirm with a point. Let's take a vertex of Figure 1: let's say (4, -5) (x=4, y=-5). Then Figure 2's corresponding vertex: x=4 - 9 = -5, y=-5 + 2 = -3. Let's check the graph: Figure 2 has a vertex around (-5, -3)? Yes, that matches. So the correct transformation is (x', y') = (x - 9, y + 2), which is option C.

Step2: Verify each option

• Option A: (x+9, y-2) would move right 9, down 2, which is opposite.
• Option B: (-y, x) is rotation, not translation.
• Option C: (x-9, y+2) moves left 9, up 2, matches the translation.
• Option D: (-x, y) is reflection over y-axis, not translation.

Answer:

C. \((x', y') = (x - 9, y + 2)\)