In order to find the distance between two points on a line, use the formula below:

$\displaystyle \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Plug in the points (6,7) and (-6,-7) and solve:

$\displaystyle \sqrt{(6+6)^{2}+(7+7)^{2}}=\sqrt{(12)^{2}+(14)^{2}}=\sqrt{144+196}=\sqrt{340}=2\sqrt{85}$

This gives a final answer of $\displaystyle 2\sqrt{85}$

Use the distance formula to determine the line connected by the two points.

The distance formula is:

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

Let:

$\displaystyle (x_1,y_1) = (2,8)$

$\displaystyle (x_2,y_2) =(-3,6)$

Substitute the points into the formula.

$\displaystyle d= \sqrt{(-3-2)^2+(6-8)^2}$

Simplify the inner terms.

$\displaystyle d= \sqrt{(-5)^2+(-2)^2}$

$\displaystyle d= \sqrt{25+4} = \sqrt{29}$

The distance of the line connect by the two points is:  $\displaystyle \sqrt{29}$

In order to find the distance between two points on a line, use the formula below:

$\displaystyle \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Plug in the points (-5,-3) and (4,2) and solve:

$\displaystyle \sqrt{(4+5)^{2}+(2+3)^{2}}=\sqrt{(9)^{2}+(5)^{2}}=\sqrt{81+25}=\sqrt{106}$

This gives a final answer of $\displaystyle \sqrt{106}$

In order to find the distance between two points on a line, use the formula below:

$\displaystyle \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Plug in the points (4,9) and (-2,-1) and solve:

$\displaystyle \sqrt{(9+1)^{2}+(4+2)^{2}}=\sqrt{(10)^{2}+(6)^{2}}=\sqrt{100+36}=\sqrt{136}$

This gives a final answer of $\displaystyle \sqrt{136}$

To find the length between two points, we use the following distance formula:

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

where $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$ are the points given.

Using the given points

$\displaystyle (1, 5)$ and $\displaystyle (-3, 4)$

we can substitute into the formula.  We get

$\displaystyle d = \sqrt{(-3-1)^2 + (4-5)^2}$

$\displaystyle d = \sqrt{(-4)^2 + (-1)^2}$

$\displaystyle d = \sqrt{16 + 1}$

$\displaystyle d = \sqrt{17}$

Therefore, the distance between the points $\displaystyle (1, 5)$ and $\displaystyle (-3, 4)$ is $\displaystyle \sqrt{17}$.

To find the length between two points, we use the following distance formula:

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

where $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$ are the points given.

Using the given points

$\displaystyle (-3, -3)$ and $\displaystyle (-5, -8)$

we can substitute into the formula.  We get

$\displaystyle d = \sqrt{(-5 - -3)^2 + (-8 - -3)^2}$

$\displaystyle d = \sqrt{(-5+3)^2 + (-8+3)^2}$

$\displaystyle d = \sqrt{(-2)^2 + (-5)^2}$

$\displaystyle d = \sqrt{4 + 25}$

$\displaystyle d = \sqrt{29}$

Therefore, the distance between the points $\displaystyle (-3, -3)$ and $\displaystyle (-5, -8)$ is $\displaystyle \sqrt{29}$.

Use the distance formula to determine the distance of this line.

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

Substitute the points into the equation.

$\displaystyle d=\sqrt{(5-3)^2+(-3-8))^2}$

Simplify the radical.

$\displaystyle d=\sqrt{(2)^2+(-11)^2} = \sqrt{4+121} = \sqrt{125}$

Pull out the common factors.  This radical can still be reduced.

$\displaystyle \sqrt{125} = \sqrt{25}\cdot \sqrt5 =5\sqrt5$

The exact length of the line is:  $\displaystyle 5\sqrt5$

The distance formula is:

$\displaystyle d= \sqrt{(x_{1}-x_{_{2}})^2+(y_{1}-y_2)^2}$

Plug in these points into the distance formula.

$\displaystyle d=\sqrt{(1-(-1))^2+(2-(-2))^2}$

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

$\displaystyle d=\sqrt{20}$

Reduce:

$\displaystyle d=\sqrt{4}*\sqrt{5}$

$\displaystyle d=2\sqrt{5}$

The distance formula is:

$\displaystyle d= \sqrt{(x_{1}-x_{_{2}})^2+(y_{1}-y_2)^2}$

Plug in Seven and Joel's coordinates into this formula.

$\displaystyle d= \sqrt{(1-(-2))^2+(2-(-2))^2}$

$\displaystyle d=\sqrt{(3^2)+4^2}$

$\displaystyle d=\sqrt{25}=5units$

Write the distance formula.

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

Substitute the given points into the formula.

$\displaystyle D=\sqrt{(7-(-3))^2+(-3-(-6))^2}$

Simplify the terms inside the parentheses.

$\displaystyle D=\sqrt{(10)^2+(3)^2} =\sqrt{100+9} = \sqrt{109}$

The answer is: $\displaystyle \sqrt{109}$