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
jeka57 [31]
3 years ago
10

3. Find the circumcenter of triangle ABC with A(1,6), B(1,4), C(5,4). (1point). a)(5,3). b)(3,5). c)(7.3). d)(1,7). 5.What is th

e name of the segment inside the large triangle?. a)perpendicular bisector. b)altitude. c)median. d)angle bisector. (I have to draw the picture for number 5)

Mathematics
2 answers:
Harrizon [31]3 years ago
6 0

For problem number 3, the answer is (3, 5). The correct answer between all the choices given is the second choice or letter B.

For problem number 5, the answer is median. The correct answer between all the choices given is the third choice or letter C.

I am hoping that these answers have satisfied your queries and it will be able to help you, and if you’d like, feel free to ask another question.

aev [14]3 years ago
4 0

Answer:

The answer is the option B

The circumcenter of triangle ABC is the point (3,5)

Step-by-step explanation:

we know that

The circumcenter of a triangle, is the point where the perpendicular bisectors of a triangle meets

In this problem we have the coordinates of the triangle ABC

A(1,6) ,B(1,4),C(5,4)

Step 1

Find the slope of the side AB

The side AB is a vertical side (parallel to the y-axis)

The slope of the side AB is undefined

we know that

The perpendicular line to the side AB will be a horizontal line (parallel to the x-axis)

The equation of the perpendicular bisector to the side AB will be the y-coordinate of the midpoint AB

Step 2

Find the y-coordinate of midpoint AB

we know that

The formula to calculate the y-coordinate of the midpoint between two points is equal to

y=\frac{y1+y2}{2}

we have

A(1,6) ,B(1,4)

Substitute the values

y=\frac{6+4}{2}=5

therefore

The equation of the perpendicular bisector to the side AB is

y=5 ------> equation A

Step 3

Find the slope of the side BC

The side BC is a horizontal side (parallel to the x-axis)

The slope of the side BC is zero

we know that

The perpendicular line to the side BC will be a vertical line (parallel to the y-axis)

The equation of the perpendicular bisector to the side BC will be the x-coordinate of the midpoint BC

Step 4

Find the x-coordinate of midpoint BC

we know that

The formula to calculate the x-coordinate of the midpoint between two points is equal to

x=\frac{x1+x2}{2}

we have

B(1,4),C(5,4)

Substitute the values

x=\frac{1+5}{2}=3

therefore

The equation of the perpendicular bisector to the side BC is

x=3 ------> equation B

Step 5

Find the circumcenter of triangle ABC

To calculate the circumcenter

Solve the system of equations compound by equation A and equation B

y=5 ------> equation A

x=3 ------> equation B

The intersection point is (3,5) -------> the circumcenter of triangle ABC

see the attached figure to better understand the problem


You might be interested in
The point (5 5/8, 2 1/4) lies on a line that represents a proportional relationship between two units of measure.
neonofarm [45]

9514 1404 393

Answer:

  a) k = 2/5

  b) y = 2/5x

  c) y = 2 3/5

Step-by-step explanation:

<h3>a)</h3>

The proportional relation is described by the equation ...

  y = kx . . . . . . k is the constant of proportionality

The value of k can be found by dividing the equation by x:

  y/x = k = (2 1/4)/(5 5/8) = (9/4)/(45/8) = 18/45

  k = 2/5

__

<h3>b)</h3>

As above, the equation is ...

  y = kx

  y = 2/5x

__

<h3>c)</h3>

Using 6.5 for x, we have ...

  y = (2/5)(6.5) = 2.6 = 2 3/5

5 0
3 years ago
Least common multiple of 35 and 70
Andreas93 [3]

Answer:

70

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
What is the fraction form of 0.3​
Masteriza [31]

Answer:

3/100

Step-by-step explanation:

Hope this helped!!!

4 0
2 years ago
Please someone help I can’t this
kupik [55]

Answer:

When i took it i chose C and was right. I'm not sure if we use the same school but it was my answer. Hope it helps.

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
2. Multiply and simplify: (x - 2)(2x + 3)<br> Answer
inysia [295]

Step-by-step explanation:

(x - 2)(2x + 3)

=2x²+3x-4x-6

=2x²-x-6

8 0
3 years ago
Read 2 more answers
Other questions:
  • The line / is tangent to the circle x^2+y^2=50 at the point A.
    6·1 answer
  • Write 9*6 as a power with a base 3
    5·1 answer
  • Answer this for me please?
    14·2 answers
  • Simplify the expression.<br> -1/2 (-5/6 + 1/3)
    6·1 answer
  • (a + b)³-(a - b)³- 6a²b
    10·2 answers
  • What is the mesure of angle AXB?
    10·2 answers
  • ?????????????????????????
    8·1 answer
  • Someone plz help me
    11·2 answers
  • WILL GIVE BRAINLIEST!
    5·2 answers
  • Ramil collected honey from 9 different beehives and recorded the amount collected, in gallons, from each hive in the line plot s
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!