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
Leya [2.2K]
1 year ago
6

(A)using geometry vocabulary, describe a sequence of transformations that maps figure P (-1,2)(-1,4) (-4,2) (-4,4) onto figure Q

(2,-2)(2,-5)(4,-2)(4,-5).(B)write the transformation mapping rules for the sequence you described in part (a).
Mathematics
1 answer:
andrey2020 [161]1 year ago
7 0

Before we proceed on determining the transformation happening on this problem, it's better to see first the location of the figure by drawing it in a cartesian coordinate plane. We have

If we observe the figures and the coordinates of the plot, we can see that there is a difference of 1 on the x coordinates of P and y coordinates of Q. Therefore, the first transformation that we consider here is the movement of figure P by 1 unit to the left. We have

\begin{gathered} P_1=(-1-1,2_{})=(-2,2) \\ P_2=(-1-1,4)=(-2,4) \\ P_3=(-4-1,2)=(-5,2) \\ P_4=(-4-1,4)=(-5,4) \end{gathered}

This transformation changes the location of figure P into

The next transformation will be the rotation of the red dotted figure on the figure above by 90 degrees counterclockwise. With this transformation, the coordinates will transform as

P_{ccw,90}=(-y,x)

Hence, for the rotation, we have the new coordinates.

\begin{gathered} P_1^{\prime}=(-2,-2) \\ P_2^{\prime}=(-4,-2) \\ P_3^{\prime}=(-2,-5) \\ P_4^{\prime}=(-4,-5) \end{gathered}

The transformed image, which is represented as NMPO, will now be at

For the last transformation, we will be reflecting the figure NMPO over the <em>y</em> axis. This changes the coordinates as

P_{\text{rotation,y}-\text{axis}}=(-x,y)

We now have the new coordinates:

\begin{gathered} P^{\doubleprime}_1=(2,-2)=Q_1_{}_{} \\ P_2^{\doubleprime}=(4,-2)=Q_3 \\ P_3^{\doubleprime}=(2,-5)=Q_2 \\ P_4^{\doubleprime}_{}=(4,-5)=Q_4_{} \end{gathered}

As you can see, they have the same coordinates as figure Q.

The mapping rules for the sequence described above are as follows:

First transformation (moving one unit to the left (x-1,y))

\begin{gathered} P_1(-1,2)\rightarrow P_1(-1-1,2)\rightarrow P_1(-2,2) \\ P_2(-1,4)\rightarrow P_1(-1-1,4)\rightarrow P_2(-2,4) \\ P_3(-4,2)\rightarrow P_1(-4-1,2)\rightarrow P_3(-5,2) \\ P_4(-4,4)\rightarrow P_1(-4-1,4)\rightarrow P_4(-5,4) \end{gathered}

Second transformation (rotation counter clockwise (-y,x))

\begin{gathered} P_1(-2,2)\rightarrow P^{\prime}_1(-2,-2)_{} \\ P_2(-2,4)\rightarrow P^{\prime}_2(-4,-2) \\ P_3(-5,2)\rightarrow P^{\prime}_3(-2,-5)_{} \\ P_4(-5,4)\rightarrow P^{\prime}_4(-4,-5)_{} \end{gathered}

Third Transformation (reflection over y-axis (-x,y))

\begin{gathered} P^{\prime}_1(-2,-2)\rightarrow P^{\doubleprime}_1(-(-2),-2)\rightarrow P^{\doubleprime}_1=(2,-2)=Q_1 \\ P^{\prime}_2(-4,-2)\rightarrow P^{\doubleprime}_1(-(-4),-2)\rightarrow P^{\doubleprime}_1=(4,-2)=Q_3 \\ P^{\prime}_3(-2,-5)\rightarrow P^{\doubleprime}_1(-(-2),-5)\rightarrow P^{\doubleprime}_1=(2,-5)=Q_2 \\ P^{\prime}_4(-4,-5)\rightarrow P^{\doubleprime}_1(-(-4),-5)\rightarrow P^{\doubleprime}_1=(4,-5)=Q_4 \end{gathered}

You might be interested in
The volume of each cone round the answer to decimal places
snow_tiger [21]

Answer:

1. 322.01

Step-by-step explanation:

Formula: v=pi X r^2(h/3)

4 0
2 years ago
How many terms in 2-8+22<br> A. 1<br> B. 2<br> C. 3<br> D. 26
natima [27]

Answer:

6 is the answer.

is it right

4 0
3 years ago
Jenny is planning an extended trip to Russia.The table below shows a list of cities which she would like to visit during her sta
densk [106]

The correct answer is D hope this helps you.

8 0
3 years ago
Read 2 more answers
Examine the following graph of a line. Which equation correctly represents the line in slope-intercept form?
Xelga [282]

Answer:

-8 -8

Step-by-step explanation:

Because it is the most reasonable

7 0
3 years ago
Two cans of paint and 1 brush cost $37. Four cans of paint and 3 brushes cost $81. Find the cost of one can of paint.
weeeeeb [17]
2c + b = 37 ....multiply by -3
4c + 3b = 81
------------------
-6c - 3b = - 111 (result of multiplying by -3)
4c + 3b = 81
------------------add
-2c = - 30
c = -30/-2
c = 15 <== $ 15 for a can of paint

and it costs $ 7 for each brush
8 0
3 years ago
Other questions:
  • A dance club hires two different DJ’s to
    15·1 answer
  • If the area of a park is exactly halfway between 2.4 and 2.5 acres, what I think area of the park
    14·2 answers
  • Sarah competes in a long jump competition.
    8·1 answer
  • Find the median of the following: 302, 220, 221, and 208. if needed, round your answer to the nearest tenth
    13·2 answers
  • Which sequence is a geometric progression?<br> A 2 4 6 8<br> B 1 1 2 3<br> С 1 2 4 8<br> D 1 3 5 7
    7·1 answer
  • −9 ≤ −3; Add 12 to both sides
    15·1 answer
  • Find the factored form of this trinomial.<br> b2 - 11b - 12
    6·1 answer
  • A boat can travel 477 miles on 53 gallons of gasoline.How much gasoline will it need to go 45 miles
    5·1 answer
  • 1. Given: C is the midpoint of AD and BE<br> Prove: AABC = ADEC<br><br> Please help
    9·1 answer
  • Surface area of a cube length: 10ft width: 7.5ft height: 12ft
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!