The reflection of a point across a line also known as the mirror line, forms an image that is equal distance from the as the preimage
The coordinates of the image following a reflection across the line x = -1 are;
R'(-2, 3), S'(-7, 4), T'(-8, -1), and U'(-3, -2)
Reason:
Question; Square RSTU with vertices R(0, 3), S(5, 4), T(6, -1), and U(1, -2), reflected about the line x = -1
Required:
To find the coordinate of the image
The line x = -1 is parallel to the y-axis, therefore, the distances of the x-coordinates of the preimage and the image from the line x = -1 are equal,
The y-coordinates of the image ang preimage are equal
The differences of distances are;
Δx, of point R (0 - (-1)) = 1, coordinates of image = R'(-1 - 1, 3) = R'(-2, 3)
Δx of point S = (5 - (-1)) = 6, coordinates of image = S'(-1 - 6, 4) = S'(-7, 4)
Δx of point T = (6 - (-1)) = 7, coordinates of image = T'(-1 - 7, -1) = T'(-8, -1)
Δx of point U = (1 - (-1)) = 2, coordinates of image = U'(-1 - 2, -2) = U'(-3, -2)
The coordinates of the vertex of image of the square RSTU following a reflection across the line x = -1 which is the square R'S'T'U' are;
R'(-2, 3), S'(-7, 4), T'(-8, -1), and U'(-3, -2)
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