Question
What kind of translation has been done to quadrilateral ABCD ? (1 point) Quadrilateral ABCD has been translated units to the right and units down.
A(2,2) B(4,6) C(4,10) D(2,6)
A(2,2) B(4,6) C(4,10) D(2,6)
Answers
GPT-4o mini
To determine the type of translation that has been applied to quadrilateral ABCD, we need to analyze the given coordinates of the vertices before and after the translation.
The original coordinates of quadrilateral ABCD are:
- A(2, 2)
- B(4, 6)
- C(4, 10)
- D(2, 6)
Let's say after translation, the new coordinates are A'(x', y'), B'(x', y'), C'(x', y'), and D'(x', y').
The problem states that quadrilateral ABCD has been translated "units to the right and units down." This means that each x-coordinate has increased by a certain value (right), while each y-coordinate has decreased by a specific value (down).
1. **Identify the translation vector:**
- "Units to the right" corresponds to an increase in x-coordinates: \((x + a, y)\)
- "Units down" corresponds to a decrease in y-coordinates: \((x, y - b)\)
So the general form of the translation can be represented as:
\[ (x, y) \rightarrow (x + a, y - b) \]
2. **Observe the new coordinates:**
We need the new coordinates after the translation to find the values of a and b. Since these values are not provided in your message, we can't directly calculate a specific translation without that information.
To calculate the translation, if you provide what the resulting coordinates are after translation, we can determine the exact values of "a" (the units right) and "b" (the units down) used for the translation of quadrilateral ABCD.
If the coordinates after translation are known, the difference in the x-coordinates will give the value of "a" and the difference in the y-coordinates will provide the value for "b" (keeping the signs in mind, since moving down will subtract from the y-coordinate).
Please provide the new coordinates so further calculations can be performed!
The original coordinates of quadrilateral ABCD are:
- A(2, 2)
- B(4, 6)
- C(4, 10)
- D(2, 6)
Let's say after translation, the new coordinates are A'(x', y'), B'(x', y'), C'(x', y'), and D'(x', y').
The problem states that quadrilateral ABCD has been translated "units to the right and units down." This means that each x-coordinate has increased by a certain value (right), while each y-coordinate has decreased by a specific value (down).
1. **Identify the translation vector:**
- "Units to the right" corresponds to an increase in x-coordinates: \((x + a, y)\)
- "Units down" corresponds to a decrease in y-coordinates: \((x, y - b)\)
So the general form of the translation can be represented as:
\[ (x, y) \rightarrow (x + a, y - b) \]
2. **Observe the new coordinates:**
We need the new coordinates after the translation to find the values of a and b. Since these values are not provided in your message, we can't directly calculate a specific translation without that information.
To calculate the translation, if you provide what the resulting coordinates are after translation, we can determine the exact values of "a" (the units right) and "b" (the units down) used for the translation of quadrilateral ABCD.
If the coordinates after translation are known, the difference in the x-coordinates will give the value of "a" and the difference in the y-coordinates will provide the value for "b" (keeping the signs in mind, since moving down will subtract from the y-coordinate).
Please provide the new coordinates so further calculations can be performed!