Question
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Reflect triangle ABC over the vertical line . What are the coordinates of vertex ?
(1 point)
x = 3 A′
The coordinates of vertex A are ( , ).
Reflect triangle ABC over the vertical line . What are the coordinates of vertex ?
(1 point)
x = 3 A′
The coordinates of vertex A are ( , ).
Answers
GPT-4o mini
To determine the coordinates of vertex A after reflecting triangle ABC over the vertical line \( x = 3 \), we first need the coordinates of point A before reflection. Let's denote the original coordinates of vertex A as \( (x_A, y_A) \).
When reflecting a point across a vertical line, we calculate the new x-coordinate using the formula:
\[
x' = 2a - x
\]
where \( a \) is the x-coordinate of the line of reflection, and \( (x, y) \) are the original coordinates of the point.
Given that the vertical line is \( x = 3 \):
- Let \( a = 3 \)
- The new x-coordinate after reflection will be:
\[
x' = 2(3) - x_A = 6 - x_A
\]
The y-coordinate remains unchanged during vertical reflection:
\[
y' = y_A
\]
Therefore, after reflection, the coordinates for vertex A' are:
\[
A' = (6 - x_A, y_A)
\]
In your question, if the coordinates of vertex A' are already given, such as \( A' = (x', y') \), you can compare and find the coordinates of vertex A by solving the equations derived above.
If you provide the specific coordinates of A' or more context, I'll be able to assist you further in determining the original coordinates of vertex A.
When reflecting a point across a vertical line, we calculate the new x-coordinate using the formula:
\[
x' = 2a - x
\]
where \( a \) is the x-coordinate of the line of reflection, and \( (x, y) \) are the original coordinates of the point.
Given that the vertical line is \( x = 3 \):
- Let \( a = 3 \)
- The new x-coordinate after reflection will be:
\[
x' = 2(3) - x_A = 6 - x_A
\]
The y-coordinate remains unchanged during vertical reflection:
\[
y' = y_A
\]
Therefore, after reflection, the coordinates for vertex A' are:
\[
A' = (6 - x_A, y_A)
\]
In your question, if the coordinates of vertex A' are already given, such as \( A' = (x', y') \), you can compare and find the coordinates of vertex A by solving the equations derived above.
If you provide the specific coordinates of A' or more context, I'll be able to assist you further in determining the original coordinates of vertex A.