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
MArishka [77]
3 years ago
7

Which sequences of transformations applied to shape I prove that shape I is similar to shape II?

Mathematics
2 answers:
Reil [10]3 years ago
8 0

Answer:

Option A and C

Step-by-step explanation:

We are given two shapes I and II.

A point in shape I is at (2,1).

The corresponding point in shape II is at (-1,-0.5).

We know that

The transformation rule when a point is reflected across x- axis is given by

(x,y)\rightarrow (x,-y)

By applying this rule on shape then we get

(2,1)\rightarrow (2,-1)

The transformation rule when a point is reflected across y- axis is given by

(x,y)\rightarrow (-x,y)

Apply this rule then we get

(2,-1)\rightarrow (-2,-1)

The transformation when a point is dilate by scale factor 0.5 is given by

(x,y)\rightarrow (0.5x,0.5y)

Now, apply dilation by scale factor 0.5

(-2,-1)\rightarrow 0.5(-2,-1)=(-1,-0.5)

Therefore, shape I transformed into shape I.

The transformation rule when a point is rotated 180 degree about origin is given by

(x,y)\rightarrow (-x,-y)

By apply this rule on shape I

Then , the coordinates of corresponding point after applying the rule

(2,1)\rightarrow (-2,-1)

Now, dilation applied on this point and the point is dilated by scale factor 0.5

Then , the coordinated of this point

(-2,-1)\rightarrow (-1,-0.5)

Therefore,  shape I transformed into shape II.

Hence,option A and C is true.

dangina [55]3 years ago
4 0

Answer:

The sequence of transformations applied to shape I is:

a. reflection across the x-axis, followed by a reflection across the y-axis, and then a dilation by a scale factor of 0.5

Step-by-step explanation:

  • Let us consider a point a (2,1) in shape I .

Now when this point is reflected across x-axis the point is transformed to:

(2,-1)

( Since the rule of transformation is:

(x,y) → (x,-y) )

Now again when this point is reflected across the y-axis the point is transformed to:

(-2,-1)

( Since the rule of transformation is:

(x,y) → (-x,y) )

Now when this point is dilated by a scale factor of 0.5 the point that is obtained is:

(-1,-0.5)

( Since, the rule of transformation is:

(x,y) → (0.5x,0.5y) )

Hence, A (2,1) → A' (-1,-0.5)

  • Similarly we will consider one more point on the shape I i.e. B(3,1)

Now when this point is reflected across x-axis the point is transformed to:

(3,-1)

( Since the rule of transformation is:

(x,y) → (x,-y) )

Now again when this point is reflected across the y-axis the point is transformed to:

(-3,-1)

( Since the rule of transformation is:

(x,y) → (-x,y) )

Now when this point is dilated by a scale factor of 0.5 the point that is obtained is:

(-1.5,-0.5)

( Since, the rule of transformation is:

(x,y) → (0.5x,0.5y) )

Hence, B (3,1) → B' (-1.5,-0.5)

Similarly all the other points of shape I could be mapped to obtain the shape II.

Hence, option: a is correct.

You might be interested in
alaska has a land area of about 1,700,000 square kliometers. florida has a land area .1 the size of alaska. what is the land are
kherson [118]
Given:
land area of Alaska: 1,700,000 square kilometers
land area of Florida: 0.10 of Alaska

To find the land area of Florida, we multiply its decimal to the land area of Alaska

1,700,000 sq. km * 0.10 = 170,000 square kilometers.

The land area of Florida is 170,000 square kilometers. It is equal to 0.10 or 10% of the land area of Alaska.<span />
8 0
3 years ago
Read 2 more answers
A recipe for leomnade calls for 1 cups of sugar and 5 cups of water. how much sugar is used per cup of water?
notka56 [123]
If one cup of sugar needs five cups water than divide the cup of water by five to get 1/5 cups sugar per cup of water :)
5 0
3 years ago
Quadrilateral PAID is a rectangle whose diagonals have the endpoints P(-3, -2)I(4, -7) and A(4, -2)D(-3, -7). Find the diagonals
BARSIC [14]

Answer:

(0.5,-4.5)

Step-by-step explanation:

The given rectangle has diagonals have the endpoints P(-3, -2) ,I(4, -7) and A(4, -2) ,D(-3, -7)

The diagonals of the rectangle bisect each other so we use the midpoint formula to find their point of intersection.

The midpoint formula is;

(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

We use any pair of endpoints of the diagonals to find the point of intersection.

Using A(4, -2) ,D(-3, -7)

(\frac{4+-3}{2},\frac{-2+-7}{2})

(\frac{1}{2},\frac{-9}{2})

or

(0.5,-4.5)

7 0
3 years ago
PLEASE HELP ASAP! PLEASE BE HONEST! ALGEBRA
ASHA 777 [7]

The answer is (2,-2)

5 0
3 years ago
Subtract. <br> Express your answer in simplest form<br><br> 3 1/4 - 2 3/4
lord [1]
The answer to this is .5 or 1/2.
3 0
3 years ago
Read 2 more answers
Other questions:
  • A piece of wood is 4 feet long. Are 4 pieces of wood longer than 4 yards?
    14·1 answer
  • A deep-sea exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is 200 feet below sea level. How de
    13·2 answers
  • Population in 1990 was 134 million. In 2000 it was 139 million. What was it in 2014
    6·1 answer
  • A soccer league has 180 players. Of those players 50% are boys. How many boys are in the soccer league?
    8·2 answers
  • Express 0.0833333 as a <br> fraction
    6·1 answer
  • Plz help me I don’t get this
    12·1 answer
  • If 12,000 people voted in the election, and 35% of them were 50-64, how many people were 50-64?
    11·2 answers
  • Which of the following equals the difference between the total surface area and base area of any three-dimensional figure?
    10·2 answers
  • WHAT WOULD THIS BEEEEE ANYONEEE!??
    13·2 answers
  • X + y = 3<br> 4x + 4y = -12
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!