All categories

2 years ago

19. Describe the sequence of transformations from quadrilateral WXYZ to W"X"Y"Z"

Mathematics

1 answer:

Tpy6a [65]2 years ago

5 0

Answer:

The sequence is as following:

1. Reflection 180°

2. Reflection over the line x=5

3. Translation 2 units down.

Step-by-step explanation:

The question is as following:

Describe the sequence of transformations from Quadrilateral WXYZ to W”X”Y”Z”.

The picture is a coordinate plane with

W= (-8,8)

X= (-2,8)

Y= (-2,4)

Z= (-8,4)

W”= (2,-10)

X”= (8,-10)

Y”= (8,-6)

Z”= (2,-6)

=================================

See the attached figure

The sequence is:

Reflection 180° ⇒ Reflection over the line x=5 ⇒ translation 2 units down.

Rule of reflection 180° is (x, y) → (–x, –y)

Rule of reflection over the line x=5 is (x, y) → (–x+10 , y)

Rule of translation 2 units down is (x, y) → (x , y–2)

The way of thinking:

1. The rectangle at the second quadrant, we need make it at the fourth quadrant, so, the suitable is Reflection 180°

2. After reflection 180°, it is noticed that we need reverse the vertices so we need to make a reflection over its vertical axis which is at x = 5

3. We need to translate it 2 units down to overlap with the required coordinates.

Check the points:

W(-8,8) ⇒ (8,-8) ⇒ (2,-8) ⇒ (2,-10)⇒W"

X(-2,8) ⇒ (2,-8) ⇒ (8,-8) ⇒ (8,-10)⇒X"

Y(-2,4) ⇒ (2,-4) ⇒ (8,-4) ⇒ (8,-6)⇒Y"

Z(-8,4) ⇒ (8,-4) ⇒ (2,-4) ⇒ (2,-6)⇒Z"

You might be interested in

The auto parts department of an automotive dealership sends out a mean of 4.34.3 special orders daily. What is the probability t

Svetlanka [38]

Answer:

$P(X = 5) = 0.166$

Step-by-step explanation:

Given

$Mean = 4.3$

$x = 5$

Required

Determine the probability that the order is 5

This question can be answered using Poisson distribution.

$P(X = x) = \frac{\alpha ^x e^{-\alpha}}{x!}$

Where

$\alpha$ is used to represent the mean

and

$\alpha = 4.3$

$x = 5$

$e = 2.71828$ ---- Euler's constant

So, we have:

$P(X = x) = \frac{\alpha ^x e^{-\alpha}}{x!}$

$P(X = 5) = \frac{4.3^5 * 2.71828^{-4.3}}{5!}$

$P(X = 5) = \frac{4.3^5 * 2.71828^{-4.3}}{5* 4 * 3 * 2 *1}$

$P(X = 5) = \frac{4.3^5 * 2.71828^{-4.3}}{120}$

$P(X = 5) = \frac{1470.08443 * 0.01356859825}{120}$

$P(X = 5) = \frac{19.9469850243}{120}$

$P(X = 5) = 0.1662248752$

$P(X = 5) = 0.166$ Approximated

6 0

3 years ago

Multiply and simplify. 2x4yx⋅6xy2z3

OLEGan [10]

Answer:

The given expression $2x^4yx \times 6xy^2z^3$ on multiplying is $12x^6y^3z^3$

Step-by-step explanation:

Consider the given two expressions $2x^4yx$ and $6xy^2z^3$

We have multiply both expressions,

$2x^4yx \times 6xy^2z^3$

To multiply two terms first multiply constant numbers that is 6 × 2 = 12

For x , y and z apply property of exponent,

$x^a\cdot x^b=x^{a+b}$

Then power of x together will be,

$x^4\cdot x\cdot x=x^{4+1+1}=x^6$

Similarly for y powers,

$y \cdot y^2=y^{1+2}=y^3$

Since first term do not have any expression for z so it will remain same.

Thus, the given expression on multiplying become,

$2x^4yx \times 6xy^2z^3$ is $12x^6y^3z^3$

7 0

3 years ago

Read 2 more answers

Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are in

dem82 [27]

There is no b unfortunately

Find inverse of x+a

x+a=y

interchAnge

y+a=x
y=x-a

Inverse is

f^{-1}x=x-a

Now

x-a=cx-d
x-cx=a-d
x(1-c)=a-d
x=a-d/1-c

You can have any number according to this but

c must not be 1
a and d must not be equal .
All three should belongs to integers set

Note:-

As there is no b given in question (May be missed in typing) Part-2 's equation can't be executed and part 3 also

5 0

2 years ago

Are the following expressions equivalent 26-(-26) and 26+(-26)

kotegsom [21]

Answer:

No.

Step-by-step explanation:

They are not because the left side is 52, while the right side is 0.

5 0

3 years ago

Evaluate the expression: 3x + 2y when X=10 and y=4

sveta [45]

Answer:

Step-by-step explanation:

3x + 2y when X=10 and y=4

3(10) + 2(4)

30 + 8

5 0

2 years ago

Read 2 more answers