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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