Question
2 trapezoids are shown. Trapezoid 1 has points A (negative 7, 0), B (negative 5, 3), C (negative 1, 3), and D (negative 1, 0). Trapezoid 2 has points A prime (1, negative 3), B prime (3, 0), C prime (7, 0), and D prime (7, negative 3).
Which rule describes the translation?
(x, y) → (x – 8, y – 3)
(x, y) → (x – 3, y + 8)
(x, y) → (x + 8, y – 3)
(x, y) → (x + 3, y + 8)
Which rule describes the translation?
(x, y) → (x – 8, y – 3)
(x, y) → (x – 3, y + 8)
(x, y) → (x + 8, y – 3)
(x, y) → (x + 3, y + 8)
Answers
GPT-4o mini
To determine the translation from trapezoid 1 to trapezoid 2, we need to analyze the coordinates of the corresponding points.
Trapezoid 1 has:
- A = (-7, 0)
- B = (-5, 3)
- C = (-1, 3)
- D = (-1, 0)
Trapezoid 2 has:
- A' = (1, -3)
- B' = (3, 0)
- C' = (7, 0)
- D' = (7, -3)
Now, let's find the change in the x and y coordinates from trapezoid 1 to trapezoid 2.
1. For point A to A':
- Change in x: 1 - (-7) = 1 + 7 = 8
- Change in y: -3 - 0 = -3
2. For point B to B':
- Change in x: 3 - (-5) = 3 + 5 = 8
- Change in y: 0 - 3 = -3
3. For point C to C':
- Change in x: 7 - (-1) = 7 + 1 = 8
- Change in y: 0 - 3 = -3
4. For point D to D':
- Change in x: 7 - (-1) = 7 + 1 = 8
- Change in y: -3 - 0 = -3
From the calculations, we see that every point translates by a change of +8 in the x-direction and -3 in the y-direction.
Thus, the translation can be represented by the rule:
\[
(x, y) \to (x + 8, y - 3)
\]
Since this is not one of your options directly without accounting for the shifts, let's adjust it.
None of the provided rules exactly match the calculated translation, but if we consider the movement based on the relative positioning of the trapezoids:
The option that includes both shifts would be:
\((x, y) \to (x + 8, y - 3)\)
However, if you strictly need it from the provided list, it appears there might be an ambiguity in how the problem is phrased or set up, as none of those specifically state the correct translation. The applicable transformation based on the analysis of the problem should still give \( (x + 8, y - 3) \) based on how we've derived the movements.
Trapezoid 1 has:
- A = (-7, 0)
- B = (-5, 3)
- C = (-1, 3)
- D = (-1, 0)
Trapezoid 2 has:
- A' = (1, -3)
- B' = (3, 0)
- C' = (7, 0)
- D' = (7, -3)
Now, let's find the change in the x and y coordinates from trapezoid 1 to trapezoid 2.
1. For point A to A':
- Change in x: 1 - (-7) = 1 + 7 = 8
- Change in y: -3 - 0 = -3
2. For point B to B':
- Change in x: 3 - (-5) = 3 + 5 = 8
- Change in y: 0 - 3 = -3
3. For point C to C':
- Change in x: 7 - (-1) = 7 + 1 = 8
- Change in y: 0 - 3 = -3
4. For point D to D':
- Change in x: 7 - (-1) = 7 + 1 = 8
- Change in y: -3 - 0 = -3
From the calculations, we see that every point translates by a change of +8 in the x-direction and -3 in the y-direction.
Thus, the translation can be represented by the rule:
\[
(x, y) \to (x + 8, y - 3)
\]
Since this is not one of your options directly without accounting for the shifts, let's adjust it.
None of the provided rules exactly match the calculated translation, but if we consider the movement based on the relative positioning of the trapezoids:
The option that includes both shifts would be:
\((x, y) \to (x + 8, y - 3)\)
However, if you strictly need it from the provided list, it appears there might be an ambiguity in how the problem is phrased or set up, as none of those specifically state the correct translation. The applicable transformation based on the analysis of the problem should still give \( (x + 8, y - 3) \) based on how we've derived the movements.