Triangle UVW has vertices at U(−2, 0), V(−3, 1), W(−3, 3). Determine the vertices of image U′V′W′ if the preimage is rotated 90° counterclockwise.

A: U′(0, −2), V′(−1, −3), W′(−3, −3)
B:U′(0, −2), V′(1, −3), W′(3, −3)
C:U′(2, 0), V′(3, −1), W′(3, −3)
D: U′(−2, 0), V′(−3, 0), W′(3, −3)

Answers

Answer 1

To find the vertices of the image after rotating 90° counterclockwise, we can use the following formula:

x' = -y
y' = x

For each vertex (x, y) in the original triangle, we can apply this formula to get the corresponding vertex in the image.

Let's start with vertex U(-2, 0):

x' = -y = 0
y' = x = -2

So, U' is at (0, -2).

Now, let's consider vertex V(-3, 1):

x' = -y = -1
y' = x = -3

So, V' is at (-1, -3).

Finally, let's consider vertex W(-3, 3):

x' = -y = -3
y' = x = 3

So, W' is at (-3, -3).

Therefore, the vertices of the image triangle U'V'W' are (0, -2), (-1, -3), and (-3, -3).

Thus, the correct answer is option A: U′(0, −2), V′(−1, −3), W′(−3, −3).

Related Questions

Which of the following sets of ordered pairs represents a function?

A: {(−4, −3), (−2, −1), (−2, 0), (0, −2), (0, 2)}
B: {(−5, −5), (−5, −4), (−5, −3), (−5, −2), (−3, 0)}
C: {(−4, −5), (−4, 0), (−3, −4), (0, −3), (3, −2)}
D: {(−6, −3), (−4, −3), (−3, −3), (−2, −3), (0, 0)}

Answers

Answer:

A set of ordered pairs represents a function if each input (first coordinate) corresponds to one and only one output (second coordinate). In other words, there can't be two different second coordinates for the same first coordinate.

Using this definition, we can determine which of the sets of ordered pairs represents a function:

A: {(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}

The input -2 has two different outputs (-1 and 0), and the input 0 also has two different outputs (-2 and 2). Therefore, this set does not represent a function.

B: {(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3, 0)}

The input -5 has four different outputs (-5, -4, -3, and -2), but each of the other inputs has only one output. Therefore, this set does not represent a function.

C: {(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}

The input -4 has two different outputs (-5 and 0), but each of the other inputs has only one output. Therefore, this set does not represent a function.

D: {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}

Each input has only one output, so this set represents a function.

Therefore, the set of ordered pairs that represent a function is D: {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.

Set C {(−4, −5), (−4, 0), (−3, −4), (0, −3), (3, −2)} does not represent a function because it has two ordered pairs with the same x-coordinate (-4). The other sets represent functions.

Can someone help me and answer this

Answers

If d represents the number of days, you can substitute 1 for d because you are trying to find how many minutes he practices per day.

The new equation would be m=60(1)

Then you just solve for m to find how many minutes and the answer is 60.

Bo practices 60 minutes per day.

Jaden made a rectangular sign that is 1.4 meters long and 1.2 meters wide to post on the wall of his store. How many square meters of wall does the sign cover? The answer is 1.68, but to solve the problem, you need to find 1.4 x 1.2(which it is 1.68). Estimate the area of wall that the sign will cover. Explain your thinking please.

Answers

To estimate the area of the wall that the sign will cover, we can use some rounding techniques to simplify the calculation.

First, we can round the dimensions of the sign to the nearest whole number to make the multiplication easier. Rounding 1.4 to 1 and 1.2 to 1, we can estimate that the sign covers approximately 1 square meter of wall.

This estimation assumes that the sign is placed directly on the wall with no gaps or overlaps. In reality, the actual area of wall covered by the sign may be slightly larger or smaller depending on the installation method and any spacing between the sign and the wall.

It's important to note that while estimation can be useful for getting a rough idea of the answer, it's not always accurate and should not be relied upon for precise calculations. In this case, using the actual dimensions of the sign to find the area of the wall covered (1.4 x 1.2 = 1.68 square meters) gives a more accurate result.

A prism is completely filled with 540 cubes that have edge length of 1/3 cm.

What is the volume of the prism?

Answers

Answer: 20

Step-by-step explanation:

Each little cube is 1/27 cm cubed. If you multiply by 540, you get 540/27. This equals 20.

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