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
jekas [21]
3 years ago
11

Instructions:Select the correct answer from each drop-down menu. ∆ABC has vertices at A(11, 6), B(5, 6), and C(5, 17). ∆XYZ has

vertices at X(-10, 5), Y(-12, -2), and Z(-4, 15). ∆MNO has vertices at M(-9, -4), N(-3, -4), and O(-3, -15). ∆JKL has vertices at J(17, -2), K(12, -2), and L(12, 7). ∆PQR has vertices at P(12, 3), Q(12, -2), and R(3, -2). can be shown to be congruent by a sequence of reflections and translations. can be shown to be congruent by a single rotation.
Mathematics
1 answer:
Akimi4 [234]3 years ago
6 0

to compare the triangles, first we will determine the distances of each side

<span>Distance = ((x2-x1)^2+(y2-y1)^2)^0.5
</span>Solving 

<span>∆ABC  A(11, 6), B(5, 6), and C(5, 17)</span>

<span>AB = 6 units   BC = 11 units AC = 12.53 units
</span><span>∆XYZ  X(-10, 5), Y(-12, -2), and Z(-4, 15)
</span><span>XY = 7.14 units   YZ = 18.79 units XZ = 11.66 units</span>

<span>∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).</span>

<span>MN = 6 units   NO = 11 units MO = 12.53 units
</span><span>∆JKL  J(17, -2), K(12, -2), and L(12, 7).
</span><span>JK = 5 units   KL = 9 units JL = 10.30 units
</span><span>∆PQR  P(12, 3), Q(12, -2), and R(3, -2)
</span><span>PQ = 5 units   QR = 9 units PR = 10.30 units</span> 
Therefore
<span>we have the <span>∆ABC   and the </span><span>∆MNO  </span><span> 
with all three sides equal</span> ---------> are congruent  
</span><span>we have the <span>∆JKL  </span>and the <span>∆PQR 
</span>with all three sides equal ---------> are congruent  </span>

 let's check

 Two plane figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (that is, by a sequence of reflections, translations, and/or rotations).

 1)     If ∆MNO   ---- by a sequence of reflections and translation --- It can be obtained ------->∆ABC 

<span> then </span>∆MNO<span> ≅</span> <span>∆ABC  </span> 

 a)      Reflexion (x axis)

The coordinate notation for the Reflexion is (x,y)---- >(x,-y)

<span>∆MNO  M(-9, -4), N(-3, -4), and O(-3, -15).</span>

<span>M(-9, -4)----------------->  M1(-9,4)</span>

N(-3, -4)------------------ > N1(-3,4)

O(-3,-15)----------------- > O1(-3,15)

 b)      Reflexion (y axis)

The coordinate notation for the Reflexion is (x,y)---- >(-x,y)

<span>∆M1N1O1  M1(-9, 4), N1(-3, 4), and O1(-3, 15).</span>

<span>M1(-9, -4)----------------->  M2(9,4)</span>

N1(-3, -4)------------------ > N2(3,4)

O1(-3,-15)----------------- > O2(3,15)

 c)   Translation

The coordinate notation for the Translation is (x,y)---- >(x+2,y+2)

<span>∆M2N2O2  M2(9,4), N2(3,4), and O2(3, 15).</span>

<span>M2(9, 4)----------------->  M3(11,6)=A</span>

N2(3,4)------------------ > N3(5,6)=B

O2(3,15)----------------- > O3(5,17)=C

<span>∆ABC  A(11, 6), B(5, 6), and C(5, 17)</span>

 ∆MNO  reflection------- >  ∆M1N1O1  reflection---- > ∆M2N2O2  translation -- --> ∆M3N3O3 

 The ∆M3N3O3=∆ABC 

<span>Therefore ∆MNO ≅ <span>∆ABC   - > </span>check list</span>

 2)     If ∆JKL  -- by a sequence of rotation and translation--- It can be obtained ----->∆PQR 

<span> then </span>∆JKL ≅ <span>∆PQR  </span> 

 d)     Rotation 90 degree anticlockwise

The coordinate notation for the Rotation is (x,y)---- >(-y, x)

<span>∆JKL  J(17, -2), K(12, -2), and L(12, 7).</span>

<span>J(17, -2)----------------->  J1(2,17)</span>

K(12, -2)------------------ > K1(2,12)

L(12,7)----------------- > L1(-7,12)

 e)      translation

The coordinate notation for the translation is (x,y)---- >(x+10,y-14)

<span>∆J1K1L1  J1(2, 17), K1(2, 12), and L1(-7, 12).</span>

<span>J1(2, 17)----------------->  J2(12,3)=P</span>

K1(2, 12)------------------ > K2(12,-2)=Q

L1(-7, 12)----------------- > L2(3,-2)=R

 ∆PQR  P(12, 3), Q(12, -2), and R(3, -2)

 ∆JKL  rotation------- >  ∆J1K1L1  translation -- --> ∆J2K2L2=∆PQR 

<span>Therefore ∆JKL ≅ <span>∆PQR   - > </span><span>check list</span></span>
You might be interested in
Write 169=13^2 in logarithmic form​
e-lub [12.9K]

Answer:

\log_{13}(169)=2

Step-by-step explanation:

The given exponential form is:

169=13^2

The base of the given expression on the right is 13 and the exponent is 2.

The number is 169.

In terms of logarithms, the base still remains the base and the exponent becomes the result of the logarithm of the number 169 to the given base 13.

\log_{13}(169)=2

4 0
2 years ago
Help giving brainliest
wolverine [178]

Answer:

Q1: 12.5

Q3: 16

IQR: 3.5

Step-by-step explanation:

Mean : 14.25

Median : 13.5

Mode : 13, 12

Range: 6

Minimum :12

Maximum: 18

Count n: 8

Sum: 114

Quartiles Quartiles:

Q1 --> 12.5

Q2 --> 13.5

Q3 --> 16

Interquartile

Range IQR: 3.5

Outliers: none

8 0
2 years ago
the sum of three numbers is 81. the second number is twice the first, and the third number is six more than the second. find the
ElenaW [278]

Answer:

have you tried using math-way just with no -

Step-by-step explanation:

3 0
2 years ago
Which of the following is an example of a quadratic equation?
WARRIOR [948]

Answer: B

Step-by-step explanation:

A quadratic equation has degree 2.

8 0
1 year ago
9. A cup of tea costs x pence. Coffee costs 20 pence more. Hermes buys 2 cups of tea and one cup of coffee. In total Hermes pays
qaws [65]

Answer:

  • £1.20

Step-by-step explanation:

<u>Given:</u>

  • Tea = x
  • Coffee = x + 0.2

<u>Comparing the total cost, work out the value of x:</u>

  • 2x + x + 0.2 = 3.80
  • 3x = 3.60
  • x = 1.20
5 0
2 years ago
Other questions:
  • Yolanda will put 70 photos ina scrapbook. She will put the same number of photos on each of 6 pages. Four photos will be in each
    13·1 answer
  • Armando read 20 pages of his 200-page book in 4 hours. At this rate, how long will it take him to read the entire book?
    5·2 answers
  • Mr. Ray wanted to measure the height of a light post. He placed a mirror on the ground 32 feet from the light post, then walked
    14·1 answer
  • Factor 2x4−5x3+6x2−15x completely over the set of integers. <br> ​
    11·1 answer
  • If the original quantity is 8 and the new quantity is 6, what is the percent decrease?
    12·1 answer
  • F(x) = x(x - 1)
    15·2 answers
  • A hair salon receives a shipment of 84 bottles of hair conditioner to use and sell to customers. The two types are labels type A
    10·1 answer
  • (NEED AN URGENT ANSWER) The sum of three consecutive integers is -96. What is the largest integer ?
    10·1 answer
  • PLZ HELP NO LINKS! WILL GIVE BRAINLIEST!
    14·2 answers
  • Write 3 + 0.3 + 0.01 + 0.002 in standard form.
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!