How do I find the slope of $(1, 2, 3)$ $(1, 2, 3)$ and $(3, 4, 5)$ $(3, 4, 5)$ ?

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How do I find the slope of $(1, 2, 3)$ $(1, 2, 3)$ and $(3, 4, 5)$ $(3, 4, 5)$ ?

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Answer 1 · 2017-07-20T22:41:29

See a solution process below:

Explanation:

Slope is defined as: $\frac{rise}{run}$ $"rise"/"run"$

Calculate Run

We can first, find the run by finding the distance between the $x$ $x$ and $y$ $y$ points using the formula for distance:

$d = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$ $d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)$

Substituting the $x$ $x$ and $y$ $y$ points gives the run as:

$d = \sqrt{{(3 - 1)}^{2} + {(4 - 2)}^{2}}$ $d = sqrt((color(red)(3) - color(blue)(1))^2 + (color(red)(4) - color(blue)(2))^2)$

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

$d = \sqrt{4 + 4}$ $d = sqrt(4 + 4)$

$d = \sqrt{8}$ $d = sqrt(8)$

$d = \sqrt{4 \cdot 2}$ $d = sqrt(4 * 2)$

$d = \sqrt{4} \sqrt{2}$ $d = sqrt(4)sqrt(2)$

$d$ $d$ or the run is $2 \sqrt{2}$ $2sqrt(2)$

Calculate Rise

In 3-dimensions the Rise is the distance between the two $z$ $z$ points:

$rise = 5 - 3 = 2$ $"rise" = 5 - 3 = 2$

Calculate Slope

$Slope = \frac{rise}{run} = \frac{2}{2 \sqrt{2}} = \frac{1}{\sqrt{2}}$ $"Slope" = "rise"/"run" = 2/(2sqrt(2)) = 1/sqrt(2)$

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How do I find the slope of $(1, 2, 3)$ $(1, 2, 3)$ and $(3, 4, 5)$ $(3, 4, 5)$ ?

1 Answer

Explanation:

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How do I find the slope of (1,2,3)(1, 2, 3) and (3,4,5)(3, 4, 5)?

1 Answer

Explanation:

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How do I find the slope of $(1, 2, 3)$ $(1, 2, 3)$ and $(3, 4, 5)$ $(3, 4, 5)$ ?