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 ​'.

(x,y)→(-x,y)

so just flip the sign of all the x-coordinates

Next time, try actually typing in your data.

 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'.

-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
  
enter your response here.

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).