The vertices of ABC are , , and . If ABC is reflected across the line y to produce the image A'B'C', find the coordinates of the vertex '.
-2,-7
The vertices of ABC are , , and . If ABC is reflected across the y-axis to produce the image ABC, find the coordinates of the vertex .
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Part 1
The coordinates of are
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To find the coordinates of the reflected vertex ', we need to understand the process of reflection and apply it to the given information.
Reflection is a transformation that produces a mirror image of a figure across a given line. In this case, the line of reflection is the y-axis.
Given that the vertices of triangle ABC are A(2, 3), B(5, 1), and C(-1, 4), we need to reflect each vertex across the y-axis to find the coordinates of the reflected vertex '.
To reflect a point across the y-axis, keep the x-coordinate the same while changing the sign of the y-coordinate.
1) Reflecting vertex A(2, 3) across the y-axis, we keep the x-coordinate the same (2) and change the sign of the y-coordinate, giving us A'(-2, -3).
2) Reflecting vertex B(5, 1) across the y-axis, we keep the x-coordinate the same (5) and change the sign of the y-coordinate, giving us B'(-5, -1).
3) Reflecting vertex C(-1, 4) across the y-axis, we keep the x-coordinate the same (-1) and change the sign of the y-coordinate, giving us C'(1, -4).
Therefore, the coordinates of the reflected vertex ' are A'(-2, -3), B'(-5, -1), and C'(1, -4).
The vertices of ABC are , , and . ABC is reflected across the y-axis and then reflected across the x-axis to produce the image A''B''C''. Graph and .
The vertices of ABC are A(-5,4), B(-2,3) and C(-4,2). If ABC is reflected across the line y=1 to produce the image A'B'C', find the coordinates of the vertex B'.
(x,y)→(-x,y)
so just flip the sign of all the x-coordinates
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