subject

Mathematics, 22.06.2019 19:10 kcain1020

If a circle has a diameter with end points: (4 + 6i) and (-2 + 6i), 1. show me how you would determine the length of the diameter and radius. 2. show me how you would determine the center of the circle. 3. determine, mathematically, if (1+9i) lies on the circle. show how you proved it mathematically. 4. determine, mathematically, if (2-i) lies on the circle. show how you proved it mathematically.

ansver

Answers: 3

Show answers

Answers

ansver

Answer from: Mathinator

Part 1) The diameter is $D=6\ units$ and the radius is equal to $r=3\ units$

Part 2) The center of the circle is (1+6i)

Part 3) The point (1+9i) lies on the circle

Part 4) The point (2-i) does not lies on the circle

Step-by-step explanation:

Part 1) Show me how you would determine the length of the diameter and radius.

we have that

The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)

we know that

The distance between the end points is equal to the diameter

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

(4 + 6i) ----> (4,6)

(-2 + 6i) ---> (-2,6)

substitute the values

$d=\sqrt{(6-6)^{2}+(-2-4)^{2}}$

$d=\sqrt{(0)^{2}+(-6)^{2}}$

$d=6\ units$

therefore

The diameter is $D=6\ units$

The radius is equal to $r=6/2=3\ units$ ---> the radius is half the diameter

Part 2) Show me how you would determine the center of the circle

we know that

The center of the circle is equal to the midpoint between the endpoints of the diameter

The circle has a diameter with end points: (4 + 6i) and (-2 + 6i)

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute

$M(\frac{4-2}{2},\frac{6+6}{2})$

M(1,6})

therefore

(1,6) ----> (1+6i)

The center of the circle is (1+6i)

Part 3) Determine, mathematically, if (1+9i) lies on the circle. Show how you proved it mathematically

Find the equation of the circle

$(x-h)^{2}+(y-k)^{2}=r^{2}$

we have

The center is (1+6i) -----> (1,6)

r=3 units

substitute

$(x-1)^{2}+(y-6)^{2}=3^{2}$

$(x-1)^{2}+(y-6)^{2}=9$

Verify if the point (1+9i) lies on the circle

Remember that

If a point lies on the circle, then the point must satisfy the equation of the circle

Substitute the value of x and the value of y in the equation and then compare the results

we have

the point (1+9i) -----> (1,9)

$(1-1)^{2}+(9-6)^{2}=9$

$(0)^{2}+(3)^{2}=9$

9=9 -----> is true

therefore

The point (1+9i) lies on the circle

Part 4) Determine, mathematically, if (2-i) lies on the circle. Show how you proved it mathematically

The equation of the circle is equal to

$(x-1)^{2}+(y-6)^{2}=9$

Verify if the point (2-i) lies on the circle

Remember that

If a point lies on the circle, then the point must satisfy the equation of the circle

Substitute the value of x and the value of y in the equation and then compare the results

we have

the point (2-i) -----> (2,-1)

$(2-1)^{2}+(-1-6)^{2}=9$

$(1)^{2}+(-7)^{2}=9$

50=9 -----> is not true

therefore

The point (2-i) does not lies on the circle

ansver

Answer from: Quest

Ithink the correct answer is d.
What is the area of the figure to the nearest tenth? a. 93.8 in^2 b. 107.2 in^2 c. 53.9 in^2 d. 23.

What is the area of the figure to the nearest tenth? a. 93.8 in^2 b. 107.2 in^2 c. 53.9 in^2 d. 23.

ansver

Answer from: Quest

addition

step-by-step explanation:

Will pay paypal money to whom answers all! answer first

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:00, sharondot2398

Sam makes his sales calls according to a pattern. he travels either north or south depending on the calendar. some of his past trips were as follows: on february 17, april 24, june 10, september 19, and november 3 he drove north. on february 28, may 25, august 22, november 20, and december 18, he drove south. describe sams' pattern. in which direction will sam drive on oct4 and oct 24?

Answers: 1

Mathematics, 21.06.2019 17:30, madelyngv97

Solve the equation - 2(m -30) = -6m a-15 b-13 c-8 d8

Answers: 1

Mathematics, 21.06.2019 18:30, joejoefofana

What is the area of the triangle 10 13 12

Answers: 1

Mathematics, 21.06.2019 19:30, auzriannamarie

Tim's phone service charges $26.39 plus an additional $0.21 for each text message sent per month. if tim's phone bill was $31.64, which equation could be used to find how many text messages, x, tim sent last month?

Answers: 1

You know the right answer?

If a circle has a diameter with end points: (4 + 6i) and (-2 + 6i), 1. show me how you would deter...

Questions in other subjects:

Konu

English, 27.03.2020 20:53

What is MacGregor's viewpoint in this passage? The Great Wave shows that Japan is a powerful nation. One copy of The Great Wave is carved on a woodblock.

Konu

Chemistry, 27.03.2020 20:53

What temperature, in C, would be required for 1.70 grams of oxygen gas (oxygen is diatomic) to occupy 9.75 liters at a pressure of 799 Torr? *...

Konu

Mathematics, 27.03.2020 20:53

If P(x) = 8x and R(x) = 9x -8, find P(x) • R(x)....

Konu

English, 27.03.2020 20:53

Which statement best describes what the authors use of the word impression connotes? A. The bed is so hard her body leaves no dents B. The beds are looked upon favorabl...

Konu

English, 27.03.2020 20:53

What do you mainly use your digital devices for?...

Konu

Physics, 27.03.2020 20:53

Somewhere on a distant planet, a simple pendulum is pulled away from the equilibrium point and released. The pendulum comes back to the point of release exactly 2.4 seconds after t...

Konu

Biology, 27.03.2020 20:53

For each glucose molecule undergoing aerobic cellular respiration in a prokaryotic cell, which on the following is incorrect a) Nitrate (NO3` ) is the final electron ac...

Konu

English, 27.03.2020 20:53

Which of the following statements best represents the model of assimilation?...

Konu

Mathematics, 27.03.2020 20:53

Riley buys office equipment with a total price of $6,280 for her new company. If the office equipment depreciates at a rate of 13% each year, which equation represents the va...

Konu

Mathematics, 27.03.2020 20:53

Darla has four buckets shaped like cylinders she is filling the buckets with water by using a scoop shaped like a cone if the cone has the same radius and the same height as the bu...

More questions: Mathematics Another questions