If there is 5280 feet in 1 mile, how may feet are in 2 miles?
1 answer:
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The coordinates of the original point <em>x</em>, can be obtained by reversing the given transformations individually
The coordinates of the original point <em>x</em> is
Reason:
The type of reflection = Glide reflection
Coordinates of the image of the point <em>x</em> = x'(3, -2)
The translation part of the glide reflection is (x, y) → (x + 3, y)
The line of reflection is y = -1
The coordinates of the original point = Required
Solution:
- A glide reflection is also known as a transflection, that involves a symmetric composite transformation of a reflection followed by a translation along the line of reflection
Reflection part;
The distance of the image point from the reflecting line = The object's
point distance from the reflecting line
Therefore, given that the reflecting line is the line y = -1, and the image
point is x'(3, -2), we have;
Distance of image from reflecting line =-1 - (-2) = 1
∴ Distance of object point from reflecting line = 1
y-coordinate of object point = -1 + 1 = 0
Point of image of the object before reflection and after translation = (3, 0)
Translation part;
The translation of the glide reflection is (x, y) → (x + 3, y)
Therefore, the location of the object before translation is ((x + 3) - 3, y), which from the point (3, 0) gives, ;
((3) - 3, 0) → (0, 0)
The coordinates of the original point <em>x</em> is
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The boat's travel from when it was first noticed until it stopped is 554.89 ft.
<h3>What is trigonometry?</h3>
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.
From the given information we can draw a right-angle triangle.
14°52' = 14 + 0.86 = 14.86 degree
45°10' = 45 + 0.16 = 45.16 degree
In the right-angle triangle ACD
tan14.86 = 200/AC
AC = 753.772 ft
In the right-angle triangle DBC:
tan45.16 = 200/CB
CB = 198.886 ft
AB = AC - CB
AB = 753.772 ft - 198.886 ft
AB = 554.886 ≈ 554.89 ft
Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.
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