\text{Find the midpoint between }\left(-3,8\right)\text{ and }\left(7,6\right) of (-3,8) , (7,6)

\textrm{Midpoint}=\left(2,7\right)

Question :

(-3,8) , (7,6)

Find the distance

d = 226

Alternative Form

d \approx 10.198039

Evaluate

(- 3, 8), (7, 6)

Let (x_{1}, y_{1}) = (- 3, 8) and (x_{2}, y_{2}) = (7, 6)

(x_{1}, y_{1}) = (- 3, 8) (x_{2}, y_{2}) = (7, 6)

Use the distance formula d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

Substitute x_{1} = - 3, y_{1} = 8 and x_{2} = 7, y_{2} = 6 into the equation

d = (7 - (- 3))^{2} + (6 - 8)^{2}

Subtract the terms

More Steps

Simplify

7 - (- 3)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

7 + 3

Add the numbers

10

d = 1 0^{2} + (6 - 8)^{2}

Subtract the numbers

d = 1 0^{2} + (- 2)^{2}

Add the numbers

More Steps

Evaluate

1 0^{2} + (- 2)^{2}

Simplify

1 0^{2} + 2^{2}

Evaluate the power

100 + 2^{2}

Evaluate the power

100 + 4

Add the numbers

104

d = 104

Solution

More Steps

Evaluate

104

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 26

Write the number in exponential form with the base of 2

2^{2} \times 26

The root of a product is equal to the product of the roots of each factor

2^{2} \times 26

Reduce the index of the radical and exponent with 2

226

d = 226

Alternative Form

d \approx 10.198039

Show Solution

Midpoint

Find the midpoint between (- 3, 8) and (7, 6)

Find the other endpoint if (- 3, 8) is the midpoint

Find the other endpoint if (7, 6) is the midpoint

Midpoint = (2, 7)

Evaluate

(- 3, 8), (7, 6)

Let (x_{1}, y_{1}) = (- 3, 8) and (x_{2}, y_{2}) = (7, 6)

(x_{1}, y_{1}) = (- 3, 8) (x_{2}, y_{2}) = (7, 6)

Use the midpoint formula Midpoint = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

Midpoint = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

Substitute x_{1} = - 3, y_{1} = 8 and x_{2} = 7, y_{2} = 6 into the equation

Midpoint = (\frac{- 3 + 7}{2}, \frac{8 + 6}{2})

Calculate

More Steps

Evaluate

\frac{- 3 + 7}{2}

Add the numbers

\frac{4}{2}

Reduce the numbers

\frac{2}{1}

Calculate

2

Midpoint = (2, \frac{8 + 6}{2})

Solution

More Steps

Evaluate

\frac{8 + 6}{2}

Add the numbers

\frac{14}{2}

Reduce the numbers

\frac{7}{1}

Calculate

7

Midpoint = (2, 7)

Show Solution

Find the slope of the line

m = - \frac{1}{5}

Evaluate

(- 3, 8), (7, 6)

The slope of the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

m = \frac{6 - 8}{7 - ( - 3 )}

Subtract the numbers

m = \frac{- 2}{7 - ( - 3 )}

Subtract the terms

More Steps

Simplify

7 - (- 3)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

7 + 3

Add the numbers

10

m = \frac{- 2}{10}

Solution

More Steps

Evaluate

\frac{- 2}{10}

Cancel out the common factor 2

\frac{- 1}{5}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{5}

m = - \frac{1}{5}

Show Solution

Find the equation of the line

Find the equation of the line through (- 3, 8) and (7, 6)

Find the equation of the line through (- 3, 8) and (7, 6) using the determinant

y = - \frac{1}{5} x + \frac{37}{5}

Evaluate

(- 3, 8), (7, 6)

The slope of the points (x_{1}, y_{1}) and (x_{2}, y_{2}) is m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

m = \frac{6 - 8}{7 - ( - 3 )}

Subtract the numbers

m = \frac{- 2}{7 - ( - 3 )}

Subtract the terms

More Steps

Simplify

7 - (- 3)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

7 + 3

Add the numbers

10

m = \frac{- 2}{10}

Divide the terms

More Steps

Evaluate

\frac{- 2}{10}

Cancel out the common factor 2

\frac{- 1}{5}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{1}{5}

m = - \frac{1}{5}

To apply the point-slope formula y - y_{1} = m (x - x_{1}),use the slope m = - \frac{1}{5} and point (- 3, 8) as (x_{1}, y_{1})

y - 8 = - \frac{1}{5} (x - (- 3))

Calculate

More Steps

Evaluate

- \frac{1}{5} (x - (- 3))

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- \frac{1}{5} (x + 3)

Apply the distributive property

- \frac{1}{5} x - \frac{1}{5} \times 3

Multiply the numbers

- \frac{1}{5} x - \frac{3}{5}

y - 8 = - \frac{1}{5} x - \frac{3}{5}

Solution

y = - \frac{1}{5} x + \frac{37}{5}

Show Solution

(-3,8) , (7,6)

Find the distance

Midpoint

Find the slope of the line

Find the equation of the line

Frequently Asked Questions

$Find the distance between (- 3, 8) and (7, 6)$ of \((-3,8) , (7,6)\)

$Find the midpoint between (- 3, 8) and (7, 6)$ of \((-3,8) , (7,6)\)

$Find the other endpoint if (- 3, 8) is the midpoint$ of \((-3,8) , (7,6)\)

$Find the other endpoint if (7, 6) is the midpoint$ of \((-3,8) , (7,6)\)

$Find the slope of the line through (- 3, 8) and (7, 6)$ of \((-3,8) , (7,6)\)

$Find the equation of the line through (- 3, 8) and (7, 6)$ of \((-3,8) , (7,6)\)

$Find the equation of the line through (- 3, 8) and (7, 6) using the determinant$ of \((-3,8) , (7,6)\)

(-3,8) , (7,6)

Find the distance

Midpoint

Find the slope of the line

Find the equation of the line

Frequently Asked Questions

Find the distance between (−3,8) and (7,6) of \((-3,8) , (7,6)\)

Find the midpoint between (−3,8) and (7,6) of \((-3,8) , (7,6)\)

Find the other endpoint if (−3,8) is the midpoint of \((-3,8) , (7,6)\)

Find the other endpoint if (7,6) is the midpoint of \((-3,8) , (7,6)\)

Find the slope of the line through (−3,8) and (7,6) of \((-3,8) , (7,6)\)

Find the equation of the line through (−3,8) and (7,6) of \((-3,8) , (7,6)\)

Find the equation of the line through (−3,8) and (7,6) using the determinant of \((-3,8) , (7,6)\)

$Find the distance between (- 3, 8) and (7, 6)$ of \((-3,8) , (7,6)\)

$Find the midpoint between (- 3, 8) and (7, 6)$ of \((-3,8) , (7,6)\)

$Find the other endpoint if (- 3, 8) is the midpoint$ of \((-3,8) , (7,6)\)

$Find the other endpoint if (7, 6) is the midpoint$ of \((-3,8) , (7,6)\)

$Find the slope of the line through (- 3, 8) and (7, 6)$ of \((-3,8) , (7,6)\)

$Find the equation of the line through (- 3, 8) and (7, 6)$ of \((-3,8) , (7,6)\)

$Find the equation of the line through (- 3, 8) and (7, 6) using the determinant$ of \((-3,8) , (7,6)\)