1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
dolphi86 [110]
3 years ago
9

How do I find the center and angle of rotation

Mathematics
1 answer:
Solnce55 [7]3 years ago
6 0

9514 1404 393

Answer:

  • B → X
  • C → Y
  • D → Z
  • 180° rotation about the origin

Step-by-step explanation:

In general, if PQ is rotated to P'Q', the center of rotation (O) will be the point of intersection of the perpendicular bisectors of PP' and QQ'. The angle of rotation will be the angle POP', or QOQ'.

__

The correspondence between preimage vertices ABCD and image vertices can be found by naming the vertices in the same order (clockwise) from one whose correspondence you know.

Here, the correspondence between A and W is given. Vertices clockwise from W are WXYZ, so those are the image points corresponding to ABCD.

__

We note that the midpoints of AW and BX are coincident at the origin. That is, the perpendicular bisectors of these segments are coincident at the origin, so the origin (point O) is the center of rotation. The rotation angle is AOW, an angle that measures 180°.

__

The image point coordinates are the opposites of the preimage point coordinates.

  A(2, 2) ⇒ W(-2, -2)

  B(2, 5) ⇒ X(-2, -5)

  C(5, 5) ⇒ Y(-5, -5)

  D(5, 2) ⇒ Z(-5, -2)

This is another indication that the rotation is 180° about the origin, since that rotation results in the mapping ...

  (x, y) ⇒ (-x, -y) . . . . . rotation 180° about the origin

You might be interested in
7 1/4 × 2²+(8 1/2-2)÷3<br>giving brainliest
lawyer [7]

Answer:

187/6

Step-by-step explanation:

Simplify the following:

(7 + 1/4) 2^2 + (8 + 1/2 - 2)/3

2^2 = 4:

(7 + 1/4) 4 + (8 + 1/2 - 2)/3

Put 7 + 1/4 over the common denominator 4. 7 + 1/4 = (4×7)/4 + 1/4:

(4×7)/4 + 1/4 4 + (8 + 1/2 - 2)/3

4×7 = 28:

(28/4 + 1/4) 4 + (8 + 1/2 - 2)/3

28/4 + 1/4 = (28 + 1)/4:

(28 + 1)/4×4 + (8 + 1/2 - 2)/3

28 + 1 = 29:

29/4×4 + (8 + 1/2 - 2)/3

29/4×4 = (29×4)/4:

(29×4)/4 + (8 + 1/2 - 2)/3

(29×4)/4 = 4/4×29 = 29:

29 + (8 + 1/2 - 2)/3

Put 8 + 1/2 - 2 over the common denominator 2. 8 + 1/2 - 2 = (2×8)/2 + 1/2 + (2 (-2))/2:

29 + ((2×8)/2 + 1/2 + (2 (-2))/2)/3

2×8 = 16:

29 + (16/2 + 1/2 + (2 (-2))/2)/3

2 (-2) = -4:

29 + (16/2 + 1/2 + (-4)/2)/3

16/2 + 1/2 - 4/2 = (16 + 1 - 4)/2:

29 + ((16 + 1 - 4)/2)/3

16 + 1 = 17:

29 + ((17 - 4)/2)/3

| 1 | 7

- | | 4

| 1 | 3:

29 + (13/2)/3

13/2×1/3 = 13/(2×3):

29 + 13/(2×3)

2×3 = 6:

29 + 13/6

Put 29 + 13/6 over the common denominator 6. 29 + 13/6 = (6×29)/6 + 13/6:

(6×29)/6 + 13/6

6×29 = 174:

174/6 + 13/6

174/6 + 13/6 = (174 + 13)/6:

(174 + 13)/6

| 1 | 7 | 4

+ | | 1 | 3

| 1 | 8 | 7:

Answer: 187/6

3 0
3 years ago
Read 2 more answers
Amy and rob each improve thier yards by pmanting rose bushes and ivy. They brought thier supplies from the same store. Amy spent
Rzqust [24]

Answer: cost of 1 pot of ivy = $12

Cost of 1 rose bush =$ 10

Step-by-step explanation:

Step 1

Let rose bushes be represented as r

and pot of ivy be represented as p

such that Amy who spent 82 dollars on 7 rose bushes and 1 pot of ivy can be expressed as

7 r + p = 82----- eqn 1

Rob who spent 74 on 5 rose bushes and 2 pots of ivy can  be expressed as

5r +2 p = 74----- eqn 2

Step 2

Solving

7 r + p = 82----- eqn 1

5r +2 p = 74----- eqn 2

By elimination method Multiply eqn 1 by 5 and eqn 2 by 7

35r+ 5p= 410--- eqn 3

35r+ 14p =518--- eqn 4

Subtracting eqn 4 from eqn 3

9p = 108

p = 108/9

p=12

p = pot of ivy = $12

therefore rose bush  wll be ( from equation 1)

7r+ p= 82

7r=82-12

7r= 70 r= 70/7

r= rose bush =$ 10

5 0
3 years ago
A fund-raiser raised $2400, which was 3/5 of the goal. Write and solve an equation to find the amount of the goal.
balu736 [363]
$4000 is the goal because if you do 2400/3= 800 so 800 x 5 = 4000
5 0
3 years ago
Which number sentences show ways to solve the problem?
Shalnov [3]

Answer:

The answer to your question is letter c and d.

Step-by-step explanation:

A.  15 × 9 = 135 and 135 – 75 = 60  This answer is not correct because it is not necessary to multiply the # members by the cost of each tree, the answer is incorrect.

B.  3 × 15 = 45 and 45 + 15 = 60  This answer is incorrect because it's using a number 3 that is not part of the data.

C.  45 ÷ 9 = 5 and 5 × 15 = 75 . This answer is correct, first finds the number of tree bought by each member and after that multiply it by the cost of each tree.

D.  45 × 15 = 675 and 675 ÷ 9 = 75 This answer is correct, first found the total cost and after divide it by the number of members.

5 0
3 years ago
The midpoint of AB is M(0,6). If the coordinates of A are (-3, 4), what are
Korolek [52]

Answer:

B(3,8)

Step-by-step explanation:

M(0,6)   A(-3,4)   B(x,y)

0=\frac{-3+x}{2}          6=\frac{4+y}{2}

0=-3+x         12=4+y

x=3               y=8

B(3,8)

3 0
4 years ago
Other questions:
  • Subtract and simplify 3g-1/9-g+1/6
    14·1 answer
  • I need help on number 11! Can anyone help?
    6·1 answer
  • For her phone service, Kala pays a monthly fee of $13 , and she pays an additional $0.05 per minute of use. The least she has be
    14·1 answer
  • A company paid $48 for 2 cases of printer paper. Each case contained 12 packages of paper. Next month the company’s office manag
    12·1 answer
  • Determine the function’s value when x = -1
    11·2 answers
  • jay can buy a stereo either online or at a local store. if he buys online, he gets 15% discount, but has to pay a $12 shipping f
    8·1 answer
  • In rhombus ABCD, AB=14 and AC=19. Find the area of the rhombus to the nearest tenth. A 190.7 B 228.3 C 195.4 D 179.8
    8·1 answer
  • A line segment has the endpoints (-7, -4) and (9,8). What are the coordinates of the midpoint
    9·2 answers
  • Christine runs each lap in 7 minutes. She will run more than 35 minutes today. What are the possible numbers of laps she will ru
    5·1 answer
  • The dinner special at Dan’s Diner comes with a choice of two side dishes, corn or potatoes, and a choice of three types of bread
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!