Is transformation an isometry ?

1 answer:

8 0

A transformation of the plane is an isometry if, for all points X and Y, the distance between the image points X' and Y' equals the distance between X and Y. In other words, an isometry is a transformation which preserves distance

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Find the hypotenuse of each isosceles right triangle when the legs are of the given measure. 6 sqrt 2

Gemiola [76]

Isosceles right triangles have two equal sides (a and b) that are not the hypotenuse (c). And when two sides are equal, so are their opposite angles. There are only 180° degrees in any triangles, thus the right angle = 90°, so 90 left for the two equal, means that 2x=90,
x = 45°.

There are several ways to go about solving a triangle like this. The best and easiest is simply to memorize that the hypotenuse is exactly root2 times the other sides. Or, each isosceles side is the hypotenuse (c) ÷ root2
$a = b = c \div \sqrt{2} \\ c = a\sqrt{2} \\ c = 6 \sqrt{2} \times \sqrt{2} = 6 \times 2 = 12$
Another way to do it is the longer proof of Pythagorean Theorem:
${c}^{2} = {a}^{2} + {b}^{2}... \: \: c = \sqrt{({a}^{2} + {b}^{2})} \\$
$c= \sqrt{({6 \sqrt{2}) }^{2} + ({6 \sqrt{2})}^{2}} \\ = \sqrt{(2 \times{(6 \sqrt{2} )}^{2} )} = \sqrt{2(36 \times 2)} \\ c = \sqrt{144} = 12$

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3 years ago

What are the domain, range, and asymptote of h(x) = 6x – 4?

Lelechka [254]

Domain: (-infinity, infinity)
Range: (-infinity, infinity)
Asymptote: none

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3 years ago

A rectangle measures 4 1/2 inches by 2 3/4 inches, what is the area of the rectangle? Answer in fraction form.

makkiz [27]

12 and 3/8 or if you want it entirely in a fraction 99/8.

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3 years ago

-4( x – 4) = 8 – 4x <br><br> last one NEED help

Ilya [14]

16=8

first you need to get rid of the parenthesis by doing distributive property which gives you -4x+16=8-4x next you cancel equal terms which is -4x so then you get

16=8 btw the equation would be false

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2 years ago

An interior designer is planning a room but needs to first figure out the dimensions. The length of the room is 23 inches on the

Lostsunrise [7]

Answer:

30.67 feet

Step-by-step explanation:

A proportion is often useful for solving scale drawing problems.

actual size : drawing size = (room length) : (23 in) = (2 ft) : (1.5 in)

Multiplying by 23 in gives ...

room length = (2 ft)(23 in)/(1.5 in) = 46/1.5 ft = 30 2/3 ft

room length ≈ 30.67 ft.

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3 years ago