Question

Find the slope and distance.
(6,-6) and (-6,+8)​

Answer 1

Hii!

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`\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}`

Slope =

Distance =

`\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}`

`\bullet` Let's work out the slope

`\twoheadrightarrow\sf \cfrac{y2-y1}{x2-x1}`

`\bullet` Stickin the values

`\twoheadrightarrow\sf \cfrac{8-(-6)}{-6-6}`

`\bullet` Simplify

`\twoheadrightarrow\sf \cfrac{8+6}{-12}`

`\bullet` Finish simplifying

`\twoheadrightarrow\sf \cfrac{14}{-12}`

`\bullet` Reduce the fraction

`\twoheadrightarrow\sf \cfrac{7}{-6}`

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`\bullet` Work out the distance

`\twoheadrightarrow\sf √((x2-x1)^2+(y2-y1)^2)`

`\bullet` Stick in the values

`\twoheadrightarrow\sf √((-6-6)^2+(8-(-6)^2)`

`\bullet` Simplify the radical expression

`\twoheadrightarrow\sf √((-12)^2+14^2)\\\\\twoheadrightarrow\sf √(144+169) \\\\\twoheadrightarrow\sf √(340)\\\\\twoheadrightarrow\sf √(85\cdot4) \quad (simplifying\,the\,surd)`

`\ddagger`
`\boldsymbol{DISTANCE=2√(85) \,Units}`
`\ddagger`

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Hope that this helped! Best wishes.

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Answer 2

`\rm slope: -(7)/(6)`

`\rm Distance: 2√(85) \ units`

Part A

`\sf slope: (y_2 - y_1)/(x_2- x_1) = (\triangle y )/(\triangle x) \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points`

Here given points are: (6, -6), (-6, 8)

Insert the values:

`\sf \rightarrow slope: (8-(-6))/(-6-6)`

`\sf \rightarrow slope: (8+ 6)/(-12)`

`\sf \rightarrow slope: (14)/(-12)`

`\sf \rightarrow slope: -(7)/(6)`

Part B

`\sf Distance \ between \ points : \sf d = √((x_2 - x_1)^2 + (y_2-y_1)^2)`

Using the formula,

`\sf d = √((-6 - 6)^2 + (8-(-6))^2)`

`\sf d = √((-12)^2 + (14)^2)`

`\sf d = √(144 +196)`

`\sf d = √(340)`

`\sf d = √(85 * 4)`

`\sf d = 2√(85)`

Hence, the distance is 2√85 units.