On a coordinate plane, 2 triangles are shown. Triangle F D E is a right triangle and has points (1, 0), (1, 3), and (5, 0). Triangle Q R P is a right triangle and has points (negative 1, negative 2), (negative 1, negative 5), and (negative 5, negative 2). Are ΔDEF and ΔRPQ congruent? Yes. ΔDEF can be mapped to ΔRPQ by a reflection across the x-axis followed by a translation 2 units left. Yes. ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down. No. ΔDEF cannot be mapped to ΔRPQ by a rigid transformation or combination of rigid transformations.

Answers

Answer 1

Answer:

Yes

ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down

Step-by-step explanation:

The coordinates of the vertices of the triangles are;

F(1, 0), D(1, 3), and E(5, 0), and Q(-1, -2), R(-1, -5), and P(-5, -2),

Length of FD = √((3 - 0)² + (1 - 1)²) = 3

Length of DE = √((5 - 1)² + (0 - 3)²) = 5

Length of FE = √((5 - 1)² + (0 - 0)²) = 4

For triangle QRP, we have;

Length of QR = √((-5 - (-2))² + (-1 - (-1))²) = 3

Length of RP = √((-5 - (-1))² + (-2 - (-4))²) = 5

Length of PQ = √((-5 - (-1))² + (-2 - (-2))²) = 4

For a reflection across the x-axis, we have;

For a rotation of 180° about the origin, we have;

For a coordinate of the preimage before reflection of (x, y), the coordinates of the image after reflection is (-x, -y)

When followed by a translation 2 units down, we have the coordinates of the image will be (-x, -y-2)

Therefore;

For the points F(1, 0), D(1, 3), and E(5, 0) on triangle FDE, we have;

Rotation 180° about the origin gives;

F(1, 0) → Rotation by 180° → F'(-1, 0)

D(1, 3) → Rotation by 180° → D'(-1, -3)

E(5, 0) → Rotation by 180° → E'(-5, 0)

For a translation 2 unites of the coordinates of the vertices of the above triangle ΔF'D'E',

F'(-1, 0) → Translation 2 units down → F''(-1, -2)

D'(-1, -3) → Translation 2 units down → D''(-1, -5)

E'(-5, 0) → Translation 2 units down → E''(-5, -2)

The coordinates of the vertices of triangle ΔF''D''E'' are equivalent to the coordinates of the ΔQRP

Therefore, ΔDEF, and ΔRPQ are congruent, because ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down.

Answer 2

Answer:

Yes

ΔDEF can be mapped to ΔRPQ by a 180° rotation about the origin followed by a translation 2 units down

Step-by-step explanation:


Related Questions

The information is in the picture

Answers

Answer:

B is correct option that helps

LOOK AT THE PICTURE
Which statement best explains if the graph correctly represents the proportional relationship y = 3.5x?


It does, the points shown on the line would be part of y = 3.5x.
It does not, proportions cannot be represented on a graph.
It does not, the points shown on the line would not be part of y = 3.5x.
It does, all proportions can be shown on the graph of this line.

Answers

Answer:

I don't think any of the answers here are right. They aren't a proportional relationship since they don't pass through the origin. So I would believe the answer would be C. Sorry if I'm wrong!!

Step-by-step explanation:

I learned about this stuff :D

Answer:

C, because you would need two numbers to find the slope of the graph.

Step-by-step explanation:

I had to take a minute to understand this question.

what are the slope and the y-intercept of the linear function that is represented by the table?

the slope is -2/5, and the y-intercept is -1/3.

the slope is -1/3, and the y-intercept is -2/5.

the slope is 1/3, and the y-intercept is -2/5.

the slope is 2/5, and the y-intercept is -1/3.

Answers

Answer:

la respuesta correcta es la letra B es decir la pendiente es -1/3 y la intersección con el eje y es -2/5 segun mis calculos

Step-by-step explanation:

The 2 triangles are congruent
JKL=PQR

Answers

Answer:

w = 3

The rest doesn't have enough information to complete, (Sorry for previous answer)

Find the values of x and y that satisfy the equation –21 + 5yi = 7x – 10i.

Answers

Answer:

The values of x and y are x = -3 and y = -2

Step-by-step explanation:

In the complex numbers if a + bi = c + di, then the real parts are equal and the imaginary parts are equal

a = cb = d

Let us use this rule to solve the question

∵ -21 + 5yi = 7x - 10i

∴ The real parts are -21 and 7x

∴ The imaginary parts are 5y and -10

∵ The real parts are equal

7x = -21

→ Divide both sides by 7

∴ [tex]\frac{7x}{7}[/tex] = [tex]\frac{-21}{7}[/tex]

x = -3

∵ The imaginary parts are equal

5y = -10

→ Divide both sides by 5

∴ [tex]\frac{5y}{5}[/tex] = [tex]\frac{-10}{5}[/tex]

y = -2

The values of x and y are x = -3 and y = -2

It is known that x1 and x2 are roots of the equation 3x^2+2x+k=0, where 2x1=−3x2. Find k.

Answers

Answer:

k = 8

Step-by-step explanation:

Since the roots of the equation 3x² + 2x + k are x₁ and x₂ and 2x₁ = 3x₂.

By the roots of an equation, ax² + bx + c , where its roots are  x₁ and x₂. It follows that sum of roots are x₁ + x₂ = -b/a and product of roots are x₁x₂ = c/a.

Comparing both equations, a = 3 b = 2 and c = k.

So, x₁ + x₂ = -b/a = -2/3 and x₁x₂ = c/a = k/3

x₁ + x₂ = -2/3 and x₁x₂ = k/3

3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k  (2)

Since 2x₁ = -3x₂, and -2x₁ = 3x₂substituting this into equations (1) and (2) above, we have

3x₁ + 3x₂ = -2 (1) and 3x₁x₂ = k  (2)

3x₁ + (-2x₁) = -2  and x₁(3x₂) = k

3x₁ - 2x₁ = -2  and x₁(3x₂) = k  

x₁ = -2  and x₁(-2x₁) = k  

x₁ = -2  and -2x₁² = k  

Substituting x₁ = -2 into -2x₁² = k, we have

-2x₁² = k

-2(-2)² = k

2(4) = k

8 = k

So, k = 8

The required value of k is -18

Given the quadratic equation [tex]3x^2+2x+k=0[/tex]

Let the roots of the equation be [tex]x_1 \ and \ x_2[/tex]

From the quadratic equatin:

a = 3, b = 3 and c = k

Sum of root = -b/a

x1 + x2 = -3/3

x1 + x2  = -1 ....................... 1

product of roots = c/a

x1x2 = k/3 ....................... 2

Recall that 2x1=−3x2

x1 = -3x2/2 ........... 3

Substitute equation 3 into 1:

x1 + x2  = -1 ....................... 1

-3x2/2 + x2 = -1

-3x2 + 2x2 = -2

-x2 = -2

x2 = 2

From equation 2:

x1x2 = k/3

2x1 = k/3

-3x2 = k/3

-3(2) = k/3

-6 = k/3

k = -18

Hence the required value of k is -18

Learn more on quadratic function here: https://brainly.com/question/11631534

Given the number 47,135,280, what is the place value of the number 3

Answers

Answer:

ten thousand

Step-by-step explanation:

Answer:

3 would be ten thousand

Step-by-step explanation:

in words it would be thirty five thousand and two hundred eighty.

the number 3 would be in the tenth thousand because its the 2nd one in the thousands. It’s the 10th thousands thats why.

In circle J with mZHLK = 18, find the mZHJK.

Answers

Answer:

The measure of angle HJK is 36°

Step-by-step explanation:

In a circle, the measure of the inscribed angle equal half the measure of the central angle subtended by the same arc

In circle J

∵ J is the center of the circle

∵ H and K lie on the circle

∠HJK is a central angle subtended by arc HK

∵ L lies on the circle

∠HLK is an inscribed angle subtended by arc HK

→ By using the rule above

∵ ∠HJK and ∠HLK are the central angle and inscribed angle

   subtended by the same arc HK

m∠HLK = [tex]\frac{1}{2}[/tex] m∠HJK

∵ m∠HLK = 18°

∴ 18 = [tex]\frac{1}{2}[/tex] m∠HJK

→ Multiply both sides by 2

∴ 36 = m∠HJK

The measure of angle HJK is 36°

okay i have two 'true or false' questions from algebra 1:

1.) "A dotted line is ordered pairs that make the equation/inequality true. True or false?"
2.) "When you have a solid line, any point in the shaded region or on the line will make the inequality true. True or false?"

Answers

1.) False
2.) True

1.) a dotted line infers that any ordered pair that comes after the line is true. Ordered pairs that fall on the line will falsify the inequality.
2.) With solid line graphed inequalities, and ordered pair on the line OR in the shaded region makes the inequality true.

You mix 2 pints of blue paint for every 5 pints of red paint to make purple paint. You use 18 pints of red paint. How much purple paint do you make?

Answers

25.2 pints of purple paint

moya picked 3 dozen apples she wents to share her apes in equal groups. show how many different way can she do this

Answers

One way is you can divide 30 by a certain amount

10 + 10 - 10 x 10 / 10

Answers

Answer:

10

Step-by-step explanation:

Thanks for the Points! Have a great day!

:)

Answer:

10 zzz

Step-by-step explanation:

Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice cream shop for $8 per hour, Leah cannot
work more than 20 hours per month
How did you determine the pair(s) (x,y) that Leah could work to meet the given conditions in item 157

Answers

Answer:

Sorry if I am wrong

Step-by-step explanation:

If you do 5x10 then you would get 50 right then if you also do 8x10 then you would get 80 add those together you get 130. that means if Leah worked 10 hours at Ice cream and 10 hours at babysitting she would not only meet her goal she would have 10 extra dollars.

What is the value x ?

Answers

Answer:

x= 62

Step-by-step explanation:

The value of a triangle is 180 degrees.

68.5+49.5= 118

180-118= 62 degrees

Please let me know wwhich is the answer! Will mark brainliest!

Answers

Answer:

A

Step-by-step explanation:

easy! it’s A ! Stay safe !!!

what is the sale price for a object that cost $75 but is on sale for 20% .

Answers

Answer:

$60

Step-by-step explanation:

$60

Step-by-step explanation:

20% = 0.2

75× 0.2 = 15

75-15=60

9.45 x 10^-5 In standard form

Answers

The answer is : 0.0000945
Hope this helped have a good day!

4879 divided by 200 as a mixed number

Answers

Answer:

Step-by-step explanation:

4879/200

is already in the simplest form. It can be written as 24.395 in decimal form.

then : 24 + 0.395

0.395 * 1000             79

_____     ____    =      __

   1           1000            200

then :  24 +  79 / 200

answer:               79

                     24--------

                          200

A movie theater sends out a coupon for ​15% off the price of a ticket. Write an equation for the​ situation, where y is the price of the ticket with the​ coupon, and x is the original price of the ticket. Use pencil and paper. The equation is y what (Use integers or decimals for any numbers in the​ expression).

Answers

Answer:

y = 0.85x

Step-by-step explanation:

Given that:

Coupon (c) = 15% off

x = original price of ticket

y = price of ticket with coupon

Price of ticket with coupon = (100 - c)% * original price)

y = (100 - 15)% * x

y = 85% * x

y = 0.85x

Which of the following is a term of -5.92?
1.45 x
2 1/4
-7.78 x with an exponent of 2
3/5

Answers

the answer is 2 1/4. could you try and help me out with my questions?

Answer:

2 1/4

Explanation

I took the test it was right.

What is the equation of the line that passes through the point (-6, 1) and has a slope of -3/2?

Answers

the equation is y=-3/2x-1

Answer:

y=-3/2x-8

Step-by-step explanation:

Which scatterplot suggests a linear relationship between x and y?

Answers

kinda looks like the second one

what is the sum of the interior angles of a heptagon ?

Answers

Let n be rhe number of vertices in the polygon, then the sum of all interior angle is (n - 2) × 180°.

Number of sides in a heptagon = 7

So, n = 7

So,

the sum of the interior angles of a heptagon

= (7 - 2) × 180°

= 5 × 180°

= 900°

Answer:

900

Step-by-step explanation:

Which expression is equivalent to 5 – 6

A. -5+ (-6)
B. 5 -(-6)
C. 6 - 5
D. - 6+5

Answers

The answer is D because -6+5= -1 and 5-6 also = -1.

Rahima goes jogging on a course that is 2.75kilometers long. If she completes the full course every morning, how many kilometers does she jog in
one week? Explain how you got your answer.

Answers

Answer:

19.25km

Step-by-step explanation:

Step one:

given data

we are told that the distance that Rahima covers on a daily is 2.75km long

we also know that a week has 7 days that is Mon-Sunday

Required

the total distance for a week

Step two:

Hence the total distance covered for  7 days is

=2.75*7

=19.25km

Simply multiply the distance covered in a day by 7 to get the distance covered in a week

Answer:

why would i go jogging on a course that is 2.75kilometers long. XD

Step-by-step explanation:

If it takes 3 1/3 minutes to fill 3/8 of a water tank, how long will it take to fill it completely?

Answers

Answer:

[tex]8 \frac{8}{9}[/tex] minutes

Step-by-step explanation:

plz mark brainlyest

If V= 1/3Bh, then what is the value of B?

Pls answer I need help with this question

Answers

Answer:

Well B is the base of the shape

If thats what you mean

Step-by-step explanation:

HELP ASAP!!! PLEASE!!! MARKING BRAINLIEST! MATH!!!

Answers

Answer:

9x50=450

Step-by-step explanation:

hope this helps

ZA and ZB are supplementary angles. If mZA = (5x
ZB (2x + 10), then find the measure of ZB.
19) and m

Answers

Answer:

i need this question too

Step-by-step explanation:

What is 25% of 167??????

Answers

Answer:

41.75

Step-by-step explanation:

Hope this helps and have a nice day :)
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