Ask question

Ask question

All categories

2 years ago

10

Which shows the image of rectangle ABCD after the rotation (x, y) → (–y, x)? On a coordinate plane, 2 rectangles are shown. The

first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (0, negative 2), B prime (0, negative 1), C prime (negative 4, negative 1), D prime (negative 4, negative 2). On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (1, negative 1), B prime (0, negative 1), C prime (0, negative 5), D prime (1, negative 5). On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (0, negative 3), B prime (0, negative 1), C prime (negative 4, negative 2), D prime (negative 4, negative 3). On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (0, negative 2), B prime (0, negative 1), C prime (4, negative 1), D prime (4, negative 2).

2 answers:

Aleonysh [2.5K]2 years ago

4 0

Answer

A on ed 2020

Step-by-step explanation:

Svetlanka [38]2 years ago

3 0

The image of the rectangle ABCD is the rectangle that has points

A' (0 , -2) , B' (0 , -1) , C' (-4 , -1) and D' (-4 , -2) ⇒ 1st answer

Step-by-step explanation:

Let us revise the cases of rotation

1. If point (x , y) rotated about the origin by angle 90° anti-clock wise

then its image is (-y , x)

2. If point (x , y) rotated about the origin by angle 180° anti-clock wise

then its image is (-x , -y)

3. If point (x , y) rotated about the origin by angle 270° anti-clock wise

then its image is (y , -x)

4. If point (x , y) rotated about the origin by angle 90° clock wise

then its image is (y , -x)

5. If point (x , y) rotated about the origin by angle 180° clock wise

then its image is (-x , -y)

6. If point (x , y) rotated about the origin by angle 270° clock wise

then its image is (-y , x)

<u><em>V.I.Note</em></u>: There is no difference between rotating 180° clockwise

or anti-clockwise around the origin

In rectangle ABCD,

∵ A = (-2 , 0)

∵ B = (-1 , 0)

∵ C = (-1 , 4)

∵ D = (-2 , 4)

∵ Rectangle ABCD is rotated by the rule (x , y) → (-y , x)

- That means 90° anti-clockwise about the origin

To find the image of each vertex change the sign of the y-coordinates

and switch x and y

∵ x-coordinate of point A = -2 and y-coordinate of point A = 0

∴ A' = (0 , -2)

∵ x-coordinate of point B = -1 and y-coordinate of point B = 0

∴ B' = (0 , -1)

∵ x-coordinate of point C = -1 and y-coordinate of point C = 4

∴ C' = (-4 , -1)

∵ x-coordinate of point D = -2 and y-coordinate of point D = 4

∴ D' = (-4 , -2)

The image of the rectangle ABCD is the rectangle that has points

A' (0 , -2) , B' (0 , -1) , C' (-4 , -1) and D' (-4 , -2)

Learn more:

You can learn more about rotation in brainly.com/question/9720317

LearnwithBrainly

You might be interested in

To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by

Anastaziya [24]

We are given equation g = 748u, where g is the total number of gallons of water used and u is the number of units.

We can see that the number of units of water being used by customers.

The number of units of water doesn't depend on the total number of gallons of water used.

Therefore, the number of units u is an independent variable.

The value of the total number of gallons is totally depends on the number of units used.

Therefore, the total number of gallons of water used g is a dependent variable.

So, we can conclude following statements:

1) g is the dependent variable.

2) u is the independent variable.

6 0

2 years ago

Read 2 more answers

Let e1= 1 0 and e2= 0 1 , y1= 4 5 , and y2= −2 7 , and let T: ℝ2→ℝ2 be a linear transformation that maps e1 into y1 and maps

Furkat [3]

Answer:

The image of $\left[\begin{array}{c}4&-4\end{array}\right]$ through T is $\left[\begin{array}{c}24&-8\end{array}\right]$

Step-by-step explanation:

We know that $T:$ $IR^{2}$ → $IR^{2}$ is a linear transformation that maps $e_{1}$ into $y_{1}$ ⇒

$T(e_{1})=y_{1}$

And also maps $e_{2}$ into $y_{2}$ ⇒

$T(e_{2})=y_{2}$

We need to find the image of the vector $\left[\begin{array}{c}4&-4\end{array}\right]$

We know that exists a matrix A from $IR^{2x2}$ (because of how T was defined) such that :

$T(x)=Ax$ for all x ∈ $IR^{2}$

We can find the matrix A by applying T to a base of the domain ( $IR^{2}$ ).

Notice that we have that data :

$B_{IR^{2}}=$ { $e_{1},e_{2}$ }

Being $B_{IR^{2}}$ the cannonic base of $IR^{2}$

The following step is to put the images from the vectors of the base into the columns of the new matrix A :

$T(\left[\begin{array}{c}1&0\end{array}\right])=\left[\begin{array}{c}4&5\end{array}\right]$ (Data of the problem)

$T(\left[\begin{array}{c}0&1\end{array}\right])=\left[\begin{array}{c}-2&7\end{array}\right]$ (Data of the problem)

Writing the matrix A :

$A=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]$

Now with the matrix A we can find the image of $\left[\begin{array}{c}4&-4\\\end{array}\right]$ such as :

$T(x)=Ax$ ⇒

$T(\left[\begin{array}{c}4&-4\end{array}\right])=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]\left[\begin{array}{c}4&-4\end{array}\right]=\left[\begin{array}{c}24&-8\end{array}\right]$

We found out that the image of $\left[\begin{array}{c}4&-4\end{array}\right]$ through T is the vector $\left[\begin{array}{c}24&-8\end{array}\right]$

3 0

2 years ago

A clothing store is analyzing merchandise prices to help make decisions on what to charge for clothing on clearance. The store o

Aleks [24]

The variable is Quantitative, has Interval level of measurement.

Variables which can be quantified & expressed numerically are Quantitative variables. Eg : as given , price

Variables which cant be qualified & expressed numerically are Qualitative variables. Eg : level of honesty, loyalty etc

Nominal & Ordinal are qualitative variables : signifying yes or no to a category (like men or women) , or ranks (x better than y) respectively. So price level is not such categorical & ordinal ratio.

Quantitative ratio variables are with reference to time , or are in forms of rate (like speed , growth per year). So, price level is not such ratio variable also.

Price is a quantitative variable, in which the ranking, its difference can be calculated. This is characteristic of a <u>Quantitative Interval Variable</u>.

4 0

2 years ago

If a1 = 6 and an = 3 + 2(an-1), then a2 equals<br><br> no links

Salsk061 [2.6K]

Answer:

15

Step-by-step explanation:

Given that a1 = 6

an = 3 + 2(an-1),

Substitute n = 2 into the formula

a2 = 3 + 2(a1)

a2 = 3 + 2(6)

a2 = 3+12

a2 = 15

Hence the second term of the sequence is 15

6 0

1 year ago

The student council raised $2,790 during its annual fundraiser. The money was shared equally among the Events Committee, the Spo

irina [24]

Answer:

77

Step-by-step explanation:

$2790 is shares equally between 3 committees. each committee would get - $2790 / 3 = $930

If a shirt costs $12 and the Sports Committee gets $930, the committee would get $930 / $12 = 77.5

The committee cannot get half a shirt, so the greatest number of shirt that can be purchased is 77

6 0

2 years ago