Question

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

Answer 1

Answer:

$\rm slope: -\dfrac{7}{6}$

$\rm Distance: 2\sqrt{85} \ units$

Part A

$\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y }{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points$

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

Insert the values:

$\sf \rightarrow slope: \dfrac{8-(-6)}{-6-6}$

$\sf \rightarrow slope: \dfrac{8+ 6}{-12}$

$\sf \rightarrow slope: \dfrac{14}{-12}$

$\sf \rightarrow slope: -\dfrac{7}{6}$

Part B

$\sf Distance \ between \ points : \sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}$

Using the formula,

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

$\sf d = \sqrt{(-12)^2 + (14)^2}$

$\sf d = \sqrt{144 +196}$

$\sf d = \sqrt{340}$

$\sf d = \sqrt{85 \times 4}$

$\sf d = 2\sqrt{85}$

Hence, the distance is 2√85 units.

Answer 2

Hii!

___________________________________________________________

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

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

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

____________________________________

$\bullet$ Work out the distance

$\twoheadrightarrow\sf \sqrt{(x2-x1)^2+(y2-y1)^2}$

$\bullet$ Stick in the values

$\twoheadrightarrow\sf \sqrt{(-6-6)^2+(8-(-6)^2}$

$\bullet$ Simplify the radical expression

$\twoheadrightarrow\sf \sqrt{(-12)^2+14^2}\\\\\twoheadrightarrow\sf \sqrt{144+169} \\\\\twoheadrightarrow\sf \sqrt{340}\\\\\twoheadrightarrow\sf \sqrt{85\cdot4} \quad (simplifying\,the\,surd)$

$\ddagger$ $\boldsymbol{DISTANCE=2\sqrt{85} \,Units}$ $\ddagger$

--

Hope that this helped! Best wishes.

--