what is the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –2/3 (x – 6) and passes thr
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Given:
The figure of a triangle DEF.
To find:
The coordinate of image of given triangle after reflection over y-axis.
Solution:
The vertices of given triangle are D(1,4), E(4,3), F(2,0).
If a figure is reflected over the y-axis, then the rule of reflection is
Using this rule, we get
Therefore, the coordinates of image are D'(-1,4), E'(-4,3) and F'(-2,0).
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:
<em>Question; Square RSTU with vertices R(0, 3), S(5, 4), T(6, -1), and U(1, -2), reflected about the line x = -1</em>
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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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