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
Andrew [12]
3 years ago
13

Right triangle ABC and its image, triangle A'B'C' are shown in the image attached.

Mathematics
1 answer:
AlladinOne [14]3 years ago
7 0

Answer:

See explanation

Step-by-step explanation:

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

(x,y)\to (y,-x)

\implies A(-3,6)\to (6,3)

\implies B(0,4)\to (4,0)

\implies C(2,6)\to (6,-2)

We apply the 90 degrees clockwise rotation rule again on the resulting points:

\implies (6,3)\to A''(3,-6)

\implies (4,0)\to B''(0,-4)

\implies (6,-2)\to C''(-2,-6)

Let us now apply 90 degrees counterclockwise  rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

(x,y)\to (-y,x)

\implies A(-3,6)\to (-6,-3)

\implies B(0,4)\to (-4,0)

\implies C(2,6)\to (-6,2)

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

\implies (-6,-3)\to A''(3,-6)

\implies (-4,0)\to B''(0,-4)

\implies (-6,2)\to C''(-2,-6)

We can see that A''(3,-6), B''(0,-4) and C''(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

You might be interested in
The circle passes through the point (−2, 3) with a center of (-4,6). What is its radius?
Ganezh [65]

Answer:

<u>radius = √13</u>

Step-by-step explanation:

Forming the equation :

<u>(x - h)² + (y - k)² = r²</u>

  • (x, y) = point on circle
  • (h, k) = center of circle
  • r = radius

Solving :

  • (-2 + 4)² + (3 - 6)² = r²
  • r² = 4 + 9
  • <u>radius = √13</u>
7 0
2 years ago
Hello!
avanturin [10]

Answer:

  • 7.71 km²

Step-by-step explanation:

<u>Area of triangle:</u>

  • A = 1/2bh

We have the value of b but not h.

Added auxiliary segments which help to find the value of h.

<em>See attached for details</em>

  • sin 40° = h/4
  • h = 4 sin 40°
  • h = 2.57 km

<u>The area is:</u>

  • A = 1/2*6*2.57 = 7.71 km²

6 0
2 years ago
Read 2 more answers
PLEASE HELP ME I HAVE MINUTES BEFORE MY COMPTER GETS TAKEN AWAY
REY [17]

47

Step-by-step explanation:

it is a vertical angle

7 0
2 years ago
Read 2 more answers
2x+2y= 24<br> x=3y<br> What is the value of x+y? I WILL MARK BRAINLIEST AND GIVE 20 POINTS.
Ivanshal [37]
Since this is a system of equations, substitute the value of x into the other equation.

2(3y)+2y=24
6y+2y=24
8y=24
y=3

x=3(3)
x=9

To check my work, substitute my x and y values:
2(9)+2(3)=24
18+6=24
24=24

Your answer is (3,9)

Hope this helps! Have a wonderful day :)
3 0
3 years ago
I NEED HELP ASAP <br> Find The Value of X
tresset_1 [31]
30

:-))))))))))))))))
3 0
3 years ago
Other questions:
  • Pharmacy wants to survey customers to find out which brand of toothpaste
    13·2 answers
  • I need help ! ASAP !
    11·1 answer
  • BRAINLIEST AND 50 PTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    6·1 answer
  • Emma has half of her investments in stock paying a 9% dividend and the other half in a stock paying 11% interest. If her total a
    5·1 answer
  • Which statement is NOT true?<br><br><br>​
    8·1 answer
  • A four-digit code can use the numbers 1, 2, 3, 4. Any of the numbers can be repeated.
    13·1 answer
  • Which measurements are accurate based on the scenario? Check all that apply.
    9·2 answers
  • Which point on the number line represents -4/5? <br> A<br> B<br> C<br> D
    15·2 answers
  • Write an equation for the line in slope intercept form
    7·1 answer
  • A mother is five times as old as her daughter. In 6 years, the mother will
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!