How many three eight inch thick books makes stack that is 6 inches tall
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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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Answer:
i. + 26x + 144 - 299 = 0
ii. x = 5
Step-by-step explanation:
The area of the figure = 299 cm²
The figure has a shape of a rectangle, so that;
Area of rectangle = length x width
length of the figure = 18 + x
width of the figure = 8 + x
Area of the figure = (18 + x) x (8 + x)
299 = (18 + x) x (8 + x)
299 = + 26x + 144
+ 26x + 144 - 299 = 0
+ 26x - 155 = 0
applying the trigonometric formula;
x = (-b ± ) ÷ 2a
= (-26 ± ) ÷ 2
= (-26 ± ) ÷ 2
= (-26 ± ) ÷ 2
= (-26 ± 36) ÷ 2
x = (-26 + 36) ÷ 2 OR x = (-26 -36) ÷ 2
= 10 ÷ 2 OR -62 ÷ 2
= 5 OR -31
Thus, x = 5