11.1 Distance and Midpoint Formulas; Circles

Before you get started, take this readiness quiz.

Find the length of the hypotenuse of a right triangle whose legs are 12 and 16 inches.
If you missed this problem, review the reference.

Factor: $x^{2} - 18 x + 81 .$
If you missed this problem, review the reference.

Solve by completing the square: $x^{2} - 12 x - 12 = 0 .$
If you missed this problem, review the reference.

Use the rectangular coordinate system to find the distance between the points $\left(6 , 1\right)$ and $\left(2 , −2\right) .$

Use the rectangular coordinate system to find the distance between the points $\left(5 , 3\right)$ and $\left(−3 , −3\right) .$

Use the Distance Formula to find the distance between the points $\left(−5 , −3\right)$ and $\left(7 , 2\right) .$

Use the Distance Formula to find the distance between the points $\left(−4 , −5\right)$ and $\left(5 , 7\right) .$

Use the Distance Formula to find the distance between the points $\left(−2 , −5\right)$ and $\left(−14 , −10\right) .$

Use the Distance Formula to find the distance between the points $\left(10 , −4\right)$ and $\left(−1 , 5\right) .$ Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

Use the Distance Formula to find the distance between the points $\left(−4 , −5\right)$ and $\left(3 , 4\right) .$ Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

Use the Distance Formula to find the distance between the points $\left(−2 , −5\right)$ and $\left(−3 , −4\right) .$ Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

Write the standard form of the equation of the circle with a radius of 6 and center $\left(0 , 0\right) .$

Write the standard form of the equation of the circle with a radius of 8 and center $\left(0 , 0\right) .$

Write the standard form of the equation of the circle with a radius of 7 and center $\left(2 , −4\right) .$

Write the standard form of the equation of the circle with a radius of 9 and center $\left(−3 , −5\right) .$

Write the standard form of the equation of the circle with center $\left(2 , 1\right)$ that also contains the point $\left(−2 , −2\right) .$

Write the standard form of the equation of the circle with center $\left(7 , 1\right)$ that also contains the point $\left(−1 , −5\right) .$

Find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

$\left(2 , 0\right)$ and $\left(5 , 4\right)$

Find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

$\left(−4 , −3\right)$ and $\left(8 , 2\right)$

Find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

$\left(−1 , 4\right)$ and $\left(2 , 0\right)$

Find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

$\left(1 , −4\right)$ and $\left(6 , 8\right)$

Find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

$\left(−3 , −5\right)$ and $\left(0 , 1\right)$

Find the distance between the points. Write the answer in exact form and then find the decimal approximation, rounded to the nearest tenth if needed.

$\left(3 , −1\right)$ and $\left(1 , 7\right)$

Write the standard form of the equation of the circle with the given radius and center $\left(0 , 0\right) .$

Radius: 7

Write the standard form of the equation of the circle with the given radius and center $\left(0 , 0\right) .$

Radius: $\sqrt{2}$

Write the standard form of the equation of the circle with the given radius and center

Radius: 1, center: $\left(3 , 5\right)$

Write the standard form of the equation of the circle with the given radius and center

Radius: $2.5 ,$ center: $\left(1.5 , −3.5\right)$

Write the standard form of the equation of the circle with the given center with point on the circle.

Center $\left(3 , −2\right)$ with point $\left(3 , 6\right)$

Write the standard form of the equation of the circle with the given center with point on the circle.

Center $\left(4 , 4\right)$ with point $\left(2 , 2\right)$

Explain the relationship between the distance formula and the equation of a circle.

In your own words, state the definition of a circle.