QuestionFind the center of the circle with diameter endpoints $(-8,2)$ and $(10,9)$ .

Studdy Solution

STEP 1

Assumptions1. The endpoints of the diameter of the circle are (-8,) and (10,9). . The center of the circle is the midpoint of the diameter.

STEP 2

We can find the center of the circle by calculating the midpoint of the diameter. The formula for the midpoint of two points $(x1, y1)$ and $(x2, y2)$ is given by $(\frac{x1 + x2}{2}, \frac{y1 + y2}{2})$

STEP 3

Now, plug in the given values for the endpoints of the diameter into the midpoint formula.
$(\frac{-8 +10}{2}, \frac{2 +9}{2})$

STEP 4

Calculate the x-coordinate of the center of the circle.
$\frac{-8 +10}{2} =1$

STEP 5

Calculate the y-coordinate of the center of the circle.
$\frac{2 +9}{2} =5.5$

STEP 6

Therefore, the center of the circle is at the point (1,5.5).

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QuestionFind the center of the circle with diameter endpoints $(-8,2)$ and $(10,9)$ .

Studdy Solution

STEP 1

Assumptions1. The endpoints of the diameter of the circle are (-8,) and (10,9). . The center of the circle is the midpoint of the diameter.

STEP 2

We can find the center of the circle by calculating the midpoint of the diameter. The formula for the midpoint of two points $(x1, y1)$ and $(x2, y2)$ is given by $(\frac{x1 + x2}{2}, \frac{y1 + y2}{2})$

STEP 3

Now, plug in the given values for the endpoints of the diameter into the midpoint formula.
$(\frac{-8 +10}{2}, \frac{2 +9}{2})$

STEP 4

Calculate the x-coordinate of the center of the circle.
$\frac{-8 +10}{2} =1$

STEP 5

Calculate the y-coordinate of the center of the circle.
$\frac{2 +9}{2} =5.5$

STEP 6

Therefore, the center of the circle is at the point (1,5.5).

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QuestionFind the center of the circle with diameter endpoints (−8,2)(-8,2)(−8,2) and (10,9)(10,9)(10,9).

Studdy Solution

STEP 1

Assumptions1. The endpoints of the diameter of the circle are (-8,) and (10,9). . The center of the circle is the midpoint of the diameter.

STEP 2

We can find the center of the circle by calculating the midpoint of the diameter. The formula for the midpoint of two points (x1,y1)(x1, y1)(x1,y1) and (x2,y2)(x2, y2)(x2,y2) is given by(x1+x22,y1+y22)(\frac{x1 + x2}{2}, \frac{y1 + y2}{2})(2x1+x2​,2y1+y2​)

STEP 3

Now, plug in the given values for the endpoints of the diameter into the midpoint formula.(−8+102,2+92)(\frac{-8 +10}{2}, \frac{2 +9}{2})(2−8+10​,22+9​)

STEP 4

Calculate the x-coordinate of the center of the circle.−8+102=1\frac{-8 +10}{2} =12−8+10​=1

STEP 5

Calculate the y-coordinate of the center of the circle.2+92=5.5\frac{2 +9}{2} =5.522+9​=5.5

STEP 6

Therefore, the center of the circle is at the point (1,5.5).

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Studdy solves anything!

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QuestionFind the center of the circle with diameter endpoints $(-8,2)$ and $(10,9)$ .

We can find the center of the circle by calculating the midpoint of the diameter. The formula for the midpoint of two points $(x1, y1)$ and $(x2, y2)$ is given by $(\frac{x1 + x2}{2}, \frac{y1 + y2}{2})$

Now, plug in the given values for the endpoints of the diameter into the midpoint formula.
$(\frac{-8 +10}{2}, \frac{2 +9}{2})$

Calculate the x-coordinate of the center of the circle.
$\frac{-8 +10}{2} =1$

Calculate the y-coordinate of the center of the circle.
$\frac{2 +9}{2} =5.5$