find the distance between the points. give an exact answer and an approximation to three decimal places

Mathematics

1 answer:

Fudgin [204]2 years ago

7 0

7.21 units is the distance between the two points.

<h3>How to find the distance between the points?</h3>

The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance between two points can be computed by measuring the length of the line segment connecting the two points.

The formula distance between the points is

$d = \sqrt{ {(y2 - y1)}^{2} + {(x2 - x1)}^{2} }$

the points are (x1 , y1) = (-6,-5)

(X2 , y2) = (-12,-9)

now, place the values of x and y in formula

$d = \sqrt{ {( - 9- ( - 5))}^{2} + {( - 12-( - 6))}^{2} } \\ d = \sqrt{ {( - 9 + 5)}^{2} + {( - 12 + 6)}^{2} }$ $d = \sqrt{ {( - 4)}^{2} + ( - 6) {}^{2} } \\ d = \sqrt{16 + 36} \\ d = \sqrt{52} \\ d = 7.21 \: units$

Hence, 7.21 units is the distance between the two points.

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Question: Find the distance between the points. give an exact answer and an approximation to three decimal places (-6,-5)&(-12,-9)

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3. From there, you could use the slope (m = -3/1) and do the "rise over run" technique.

The only difference is going 3 units down (rise), and 1 unit to the right (run).
You'll also go 3 units up (rise), 1 unit to the left (run).
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4. Once you create a line, you'll have to choose a test point to see which region of the plane you need to shade. Let's choose the point of origin, (0, 0).

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0 > 1 (False statement, because 0 is not greater than 1).

Therefore, you'll have to shade the region where it doesn't contain the point, (0, 0) (shade the right side of the region).

Attached is the screenshots of the graph I created. The first one shows how I did step #3, where I started with plotting the y-intercept, (0, 1) and used the slope to plot other points and create the line. The 2nd screenshot is the final graph, where it shows the shaded region.

Hope this helps :)