Solved on Sep 19, 2023

Find the mathematical relationship between the points $(8,6)$ and $(3,-6)$ , such as the distance or slope of the line.

STEP 1

Assumptions1. We have two points in a-dimensional space $(8,6)$ and $(3,-6)$ . We are looking for a mathematical relationship between these points, which could be the distance between them, the slope of the line passing through them, or another mathematical operation.

STEP 2

First, let's calculate the distance between these points using the Euclidean distance formula. The formula is given by $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, plug in the given values for the coordinates to calculate the distance.
$Distance = \sqrt{(3 -8)^2 + (-6 -6)^2}$

STEP 4

Calculate the distance between the points.
$Distance = \sqrt{(-)^2 + (-12)^2} = \sqrt{25 +144} = \sqrt{169} =13$

STEP 5

Now, let's calculate the slope of the line passing through these points. The formula for the slope is given by $lope = \frac{y2 - y1}{x2 - x1}$

STEP 6

Now, plug in the given values for the coordinates to calculate the slope.
$lope = \frac{-6 -6}{3 -8}$

STEP 7

Calculate the slope of the line passing through the points.
$lope = \frac{-12}{-5} =2.4$ So, the distance between the points $(,6)$ and $(3,-6)$ is13 units, and the slope of the line passing through these points is2.4.

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Find the mathematical relationship between the points $(8,6)$ and $(3,-6)$ , such as the distance or slope of the line.

STEP 1

Assumptions1. We have two points in a-dimensional space $(8,6)$ and $(3,-6)$ . We are looking for a mathematical relationship between these points, which could be the distance between them, the slope of the line passing through them, or another mathematical operation.

STEP 2

First, let's calculate the distance between these points using the Euclidean distance formula. The formula is given by $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

STEP 3

Now, plug in the given values for the coordinates to calculate the distance.
$Distance = \sqrt{(3 -8)^2 + (-6 -6)^2}$

STEP 4

Calculate the distance between the points.
$Distance = \sqrt{(-)^2 + (-12)^2} = \sqrt{25 +144} = \sqrt{169} =13$

STEP 5

Now, let's calculate the slope of the line passing through these points. The formula for the slope is given by $lope = \frac{y2 - y1}{x2 - x1}$

STEP 6

Now, plug in the given values for the coordinates to calculate the slope.
$lope = \frac{-6 -6}{3 -8}$

STEP 7

Calculate the slope of the line passing through the points.
$lope = \frac{-12}{-5} =2.4$ So, the distance between the points $(,6)$ and $(3,-6)$ is13 units, and the slope of the line passing through these points is2.4.

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Find the mathematical relationship between the points (8,6)(8,6)(8,6) and (3,−6)(3,-6)(3,−6), such as the distance or slope of the line.

STEP 1

Assumptions1. We have two points in a-dimensional space (8,6)(8,6)(8,6) and (3,−6)(3,-6)(3,−6). We are looking for a mathematical relationship between these points, which could be the distance between them, the slope of the line passing through them, or another mathematical operation.

STEP 2

First, let's calculate the distance between these points using the Euclidean distance formula. The formula is given byDistance=(x2−x1)2+(y2−y1)2Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}Distance=(x2−x1)2+(y2−y1)2​

STEP 3

Now, plug in the given values for the coordinates to calculate the distance.Distance=(3−8)2+(−6−6)2Distance = \sqrt{(3 -8)^2 + (-6 -6)^2}Distance=(3−8)2+(−6−6)2​

STEP 4

Calculate the distance between the points.Distance=(−)2+(−12)2=25+144=169=13Distance = \sqrt{(-)^2 + (-12)^2} = \sqrt{25 +144} = \sqrt{169} =13Distance=(−)2+(−12)2​=25+144​=169​=13

STEP 5

Now, let's calculate the slope of the line passing through these points. The formula for the slope is given bylope=y2−y1x2−x1lope = \frac{y2 - y1}{x2 - x1}lope=x2−x1y2−y1​

STEP 6

Now, plug in the given values for the coordinates to calculate the slope.lope=−6−63−8lope = \frac{-6 -6}{3 -8}lope=3−8−6−6​

STEP 7

Calculate the slope of the line passing through the points.lope=−12−5=2.4lope = \frac{-12}{-5} =2.4lope=−5−12​=2.4So, the distance between the points (,6)(,6)(,6) and (3,−6)(3,-6)(3,−6) is13 units, and the slope of the line passing through these points is2.4.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the mathematical relationship between the points $(8,6)$ and $(3,-6)$ , such as the distance or slope of the line.

Assumptions1. We have two points in a-dimensional space $(8,6)$ and $(3,-6)$ . We are looking for a mathematical relationship between these points, which could be the distance between them, the slope of the line passing through them, or another mathematical operation.

First, let's calculate the distance between these points using the Euclidean distance formula. The formula is given by $Distance = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

Now, plug in the given values for the coordinates to calculate the distance.
$Distance = \sqrt{(3 -8)^2 + (-6 -6)^2}$

Calculate the distance between the points.
$Distance = \sqrt{(-)^2 + (-12)^2} = \sqrt{25 +144} = \sqrt{169} =13$

Now, let's calculate the slope of the line passing through these points. The formula for the slope is given by $lope = \frac{y2 - y1}{x2 - x1}$

Now, plug in the given values for the coordinates to calculate the slope.
$lope = \frac{-6 -6}{3 -8}$

Calculate the slope of the line passing through the points.
$lope = \frac{-12}{-5} =2.4$ So, the distance between the points $(,6)$ and $(3,-6)$ is13 units, and the slope of the line passing through these points is2.4.