Write a Doubles fact you can use to find the sum. Write the sum 2+3

9. Two points in the plane, A(−3,8) and ????(17,8), represent the endpoints of the diameter of a circle.

kherson [118]

Answer:

a) (7,8)

b) r = 10

c) $(x-7)^2+(y-8)^2=100$

Step-by-step explanation:

a) Given the endpoints the diameter of the circle as A(-3,8) and B(17,8)

we should realize that the center of the circle lies exactly at the midpoint of these two points. let's denote the midpoint as $(x_m,y_m)$

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{-3+17}{2},\dfrac{8+8}{2}\right)$

$(x_m, y_m) = (7,8)$

this is the coordinate of the center of the circle.

b) The radius of the circle can be easily found by using the distance formula between the center point and either of the two endpoints of the diameter.

the general distance formula is:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

in our case the equation changes to: (selecting the centre and point B)

$r = \sqrt{(x_m-x_2)^2+(y_m-y_2)^2}$

$r = \sqrt{(7-17)^2+(8-8)^2}$

$r = 10$

side note: there are more alternate ways to find the radius for e.g (you can use the distance formula between the points A and B and that'll give you the length of the diameter which you can divide by 2 to get the radius) OR (you don't need to use the distance formula at all <u>since in this particular case</u> all the coordinates lie on the same horizontal line, so by simply subtracting the two x-coordinates of the center and either of A or B)

c) the ingredients needed to make the equation of the circle are the

coordinates of the center: $(x_m,y_m) = (7,8)$
radius of the circle: $r = 10$

we can put this in the formula of the circle:

$(x-a)^2+(y-b)^2=r^2$

in our case the equation changes to:

$(x-x_m)^2+(y-y_m)^2=r^2$

$(x-7)^2+(y-8)^2=(10)^2$

$(x-7)^2+(y-8)^2=100$

this is the equation of the circle!

6 0

3 years ago

Simplify<br>answer it<br>b)

exis [7]

Answer:

a) 8x + 5x = 13x

b) 9f + 10f - 12f = 7f

Step-by-step explanation:

For part b, just solve from left to right normally, since adding and subtracting are inverse operations. (Inverse operation; meaning they are opposites of each other.)

So 9 + 10 = 19, and 19 - 12 = 7.

Hope this helps you :)

3 0

2 years ago

Read 2 more answers

Arturo bought a cabin by a lake for $39,439. Jake bought the cabin next door. Arturo paid $10,430 less for his cabin than Jake.

Len [333]

D is the right answer you just have to minus

5 0

3 years ago

You hike 1.2 miles west from a trailhead and then receive a text from a friend. She

alexira [117]

Answer:

the answer is definitely 4

5 0

2 years ago

Write an equation of the line that is parallel to 5x+20y=10 and passes through the point (8,3).

avanturin [10]

Answer:

20y = -5x + 10

y = -1/4x + 1/2

y - 3 = -1/4(x - 8)

y - 3 = -1/4x + 2

y = -1/4x + 5

Step-by-step explanation:

7 0

3 years ago