Question

The vertices of AABC are A(-4,5), B(-2,3), and C(-3,3). If AABC is reflected across the line y = 1 to produce the image AA'B'C', find the coordinates of the vertex
C'
The coordinates of C' after a reflection across the line y = 1 are 1
(Type an ordered pair)

Answer 1

The distances of the preimage and the image from the line of reflection are equal

The coordinates of C' after a reflection across the line y = 1 are (-3, -1)

The reason the above value is correct is as follows:

The given vertices of the ΔABC are; A(-4, 5), B(-2, 3) and C(-3, 3)

The line of reflection to produce the image ΔA'B'C' is the line y = 1

Required:

To find the coordinates of C' after a reflection across the line y = 1

Solution:

Let (x, y) represent the coordinate of the point C

x-coordinate value:

The line y = 1 is parallel to the x-axis, therefore, the x-value will remain the same following a reflection across the x-axis

Taking the point C' as the image of the corresponding point C(-3, 3), we have that the x-coordinate of the point C' is also -3

x = -3

y-coordinate value:

The difference between the coordinate of the preimage and the reflecting line is the same as the difference between the reflecting line and the coordinates of the image

The y-value distance of the point C(-3, 3), from the line y = 1 is 3 - 1 = 2

Therefore, the y-value  distance of C' from the reflecting line is given as follows;

1 - y = 2

y = 1 - 2 = -1

y = -1

Therefore, the coordinates of the point C' is (x, y) = (-3, -1)

Learn more about reflection transformation here:

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