Mathematics, 12.10.2019 01:30 kkeith121p6ujlt

Atriangle is rotated 90° about the origin. which rule describes the transformation?
(x, y) → (–x, –y)
(x, y) → (–y, x)
(x, y) → (–y, –x)
(x, y) → (y, –x)

Answers: 2

Show answers

Answers

Answer from: 20calzoy

$\boxed{ \ (x, y) \rightarrow (-y, x) \ }$

Further explanation

We already know there are four types of transformation geometry: Translation, Reflection, Rotation, and Dilation.

Rotation represents a type of transformation in which a figure is rotated about fixed points called centers of rotation. The result of rotation is the same shape and size, but the figures may be turned in different directions. Rotations may be clockwise or counterclockwise. A positive angle of rotation moves the figure counterclockwise, and a negative angle turns the figure clockwise. Without being mentioned, it means a positive angle.

However, we must moreover know about the use of multiplier matrices in transformation geometry. The matrix used in rotation 90° in the counterclockwise direction, in other words, a positive angle 90°, is

$\left[\begin{array}{ccc}0&-1\\1&0\\\end{array}\right]$

State (x, y) as the initial coordinate and (x', y') as the final coordinate.

The results of rotation are obtained from the multiplication of the matrix with the initial coordinates.

$\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}0&-1\\1&0\\\end{array}\right]\left[\begin{array}{ccc}x\\y\\\end{array}\right]$

$\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}(0)(x) + (-1)(y)\\(1)(x) + (0)(y)\\\end{array}\right]$

$\left[\begin{array}{ccc}x'\\y'\\\end{array}\right] = \left[\begin{array}{ccc}-y\\x\\\end{array}\right]$

It can be concluded that if a point is rotated 90° about the origin, the rule that describes the transformation is $\boxed{ \ (x, y) \rightarrow (-y, x) \ }$

Example:

Triangle ABC with coordinates of points A (3, 2), B (6, 2), and C (3, 6) is rotated 90 about the origin. The points of rotation results are called A', B', and C'.

Let's find out the rotation results called A', B', and C' implementing the rule above.

$\boxed{ \ A(3, 2) \rightarrow A'(-2, 3) \ }$

$\boxed{ \ B(6, 2) \rightarrow B'(-2, 6) \ }$

$\boxed{ \ C(3, 6) \rightarrow C'(-6, 3) \ }$

Learn moreThe similar problem A dilation is NOT rigid motion transformation The type of transformation applied in figure

Keywords: triangle, rotated, rotation, 90 degrees, about the origin, transformation geometry, translation, reflection, dilation, multiplier matrix, initial coordinate, rule, describes

Atriangle is rotated 90° about the origin. which rule describes the transformation? (x, y) → (–x, –

Answer from: Quest

You're gonna need to post the table

Answer from: Quest

the required function is $y=-x+4$ .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-7}{)}=\frac{-3}{3}=-1$

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

$y=mx+b$

where, m is slope and b is y-intercept.

$y=-1x+4$

$y=-x+4$

therefore the required function is $y=-x+4$ . the graph of this function is shown below.

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Find an equation for the linear function which has slope -10 and x-intercept -7

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

The probability that you roll a two on a six-sided die is 1 6 16 . if you roll the die 60 times, how many twos can you expect to roll

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

The graph shows the charges for a health club in a month. make a function table for the input-output values. writes an equation that can be used to find the total charge y for the number of x classes

Answers: 2

Answer

Mathematics, 21.06.2019 23:00

Someone answer this asap for the function f(x) and g(x) are both quadratic functions. f(x) = x² + 2x + 5 g(x) = x² + 2x - 1 which statement best describes the graph of g(x) compared to the graph of f(x)? a. the graph of g(x) is the graph of f(x) shifted down 1 units. b. the graph of g(x) is the graph of f(x) shifted down 6 units. c. the graph of g(x) is the graph of f(x) shifted to the right 1 unit. d. the graph of g(x) is the graph of f(x) shifted tothe right 6 units.

Answers: 3

Answer

You know the right answer?

Atriangle is rotated 90° about the origin. which rule describes the transformation?
(x, y) →...

Questions