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
Nastasia [14]
3 years ago
12

Find the coordinates of the circumcenter of triangle ABC with vertices A(1,4) B(1,2) and C(6,2)

Mathematics
2 answers:
zloy xaker [14]3 years ago
7 0

Answer:

D. (3.5, 3)

Step-by-step explanation:

Just something simple

Ray Of Light [21]3 years ago
6 0
<span>(3.5, 3) is the circumcenter of triangle ABC. The circumcenter of a triangle is the intersection of the perpendicular bisectors of each side. All three of these perpendicular bisectors will intersect at the same point. So you have a nice self check to make sure your math is correct. Now let's calculate the equation for these bisectors. Line segment AB: Slope (4-2)/(1-1) = 2/0 = infinity. This line segment is perfectly vertical. So the bisector will be perfectly horizontal, and will pass through ((1+1)/2, (4+2)/2) = (2/2, 6/2) = (1,3). So the equation for this perpendicular bisector is y = 3. Line segment BC (2-2)/(6-1) = 0/5 = 0 This line segment is perfectly horizontal. So the bisector will be perfectly vertical, and will pass through ((1+6)/2,(2+2)/2) = (7/2, 4/2) = (3.5, 2) So the equation for this perpendicular bisector is x=3.5 So those two bisectors will intersect at point (3.5,3) which is the circumcenter of triangle ABC. Now let's do a cross check to make sure that's correct. Line segment AC Slope = (4-2)/(1-6) = 2/-5 = -2/5 The perpendicular will have slope 5/2 = 2.5. So the equation is of the form y = 2.5*x + b And will pass through the point ((1+6)/2, (4+2)/2) = (7/2, 6/2) = (3.5, 3) Plug in those coordinates and calculate b. y = 2.5x + b 3 = 2.5*3.5 + b 3 = 8.75 + b -5.75 = b So the equation for the 3rd bisector is y = 2.5x - 5.75 Now let's check if the intersection with this line against the other 2 works. Determining intersection between bisector of AC and AB y = 2.5x - 5.75 y = 3 3 = 2.5x - 5.75 8.75 = 2.5x 3.5 = x And we get the correct value. Now to check AC and BC y = 2.5x - 5.75 x = 3.5 y = 2.5*3.5 - 5.75 y = 8.75 - 5.75 y = 3 And we still get the correct intersection.</span>
You might be interested in
Compute the value of the discriminant and give the number of real solutions of the quadratic equation.
Sergio039 [100]
-2x^2+6x-3=0 \\ \\&#10;a=-2 \\ b=6 \\ c=-3 \\ \Delta=b^2-4ac=6^2-4 \times (-2) \times (-3)=36-24=12

The value of the discriminant is 12.
Since the discriminant is greater than zero, the equation has two real solutions.
4 0
3 years ago
THANK YOU , PLEASE INCLUDE EXPLANATION
frosja888 [35]

Remark

This will be a little late, but I'll answer it anyway. The more you see of the sine law, the clearer it will be.


Step One

Set up the sine Law.

\dfrac{Sin(x)}{12}=\dfrac{sin(75)}{22}


Step Two

Substitute values

Sin(x) = ??

sin(75) = 0.9659


\dfrac{Sin(x)}{12}=\dfrac{0.9659}{22}


Step Three

Cross multiply and Solve

22* Sin(x) = 12 * 0.9659

22* Sin(x) = 11.591 divide by 22

sin(x) = 11.591 / 22

sin(x) = 0.5269


Step Four

You have to know how to use the inverse of an angle to get the answer. I do it as my calculator would do it. If it doesn't work with yours, let me know.


x = sin^-1(0.5269)

2nd F

Sin^-1

(

0.5269

)

=

You should get 31.79 degrees.

5 0
3 years ago
Please help me i really need help please help please
solong [7]

Answer:

3.605 ft is the answer.

Step-by-step explanation:

Applying Pythagoras theorem,

a^2 + b^2 = c^2

2^2 + 3^2 = c^2

4 + 9 = c^2

13 = c^2

3.605 = c

therefore, the answer is 3.605.

:)

8 0
3 years ago
Todd begins piano practice ar 4:15 p.m. and ends at 5:50 p.m. How long does he practice
kumpel [21]
He practiced for 1 hour and 30 minutes
4 0
3 years ago
Read 2 more answers
If m + n = 7 and 2n - 3m = 6, what is the value of 3n - 2m ?
S_A_V [24]
Since m + n = 7 we know m = 7-n. So now we have 2n - 3(7-n) = 6. From this we get n = -3. So now we know m - 3 = 7 so m = 10. So now we have 3(-3) + 2(10) = ? and this comes out as 11
8 0
3 years ago
Read 2 more answers
Other questions:
  • If 3 quarts are divided into 16 players how many ounces each player get
    10·1 answer
  • An interior angle of a regular polygon has a measure of 135° how many sides does it have
    9·1 answer
  • Roduct.<br> 93 + (68 + 7)
    12·2 answers
  • If the area of an equilateral triangle with sides of 4 ft. is 4 to the square root of 3 power, then the area of the regular hexa
    14·1 answer
  • If f(x)=1/x+2 what is f(3+h)?
    9·1 answer
  • Can you give me the answers to the picture i showed u
    8·2 answers
  • A scale drawing of a boat is 15 centimeters long. If the drawing uses a scale of 1 centimeter = 1.5 feet, how long many feet lon
    14·1 answer
  • What is the gcf of 36, 126, and 210?
    11·2 answers
  • Define a variable and write an equation to find each number. Then solve.
    13·1 answer
  • How to answer this question ?<br>​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!