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Mathematics 26 Online
OpenStudy (anonymous):

What is the distance between the origin of a Cartesian coordinate system and the point (5, -2)? If necessary, round your answer to two decimal places.

OpenStudy (whpalmer4):

Origin is at \((0,0)\) Distance between two points \((x_1,y_1) \text{ and } (x_2,y_2)\) is\[d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\]

OpenStudy (whpalmer4):

|dw:1393631247762:dw|

OpenStudy (anonymous):

where would i plug them in?

OpenStudy (whpalmer4):

|dw:1393631302638:dw| You've got a right triangle with sides of length (5-0)=5 and (0-(-2)) = 2

OpenStudy (whpalmer4):

One of your points is \((0,0)\). Call it \((x_1,y_1)\). The other point is \((5,-2)\). Call it \((x_2,y_2)\). Plug the numbers into my formula.

OpenStudy (anonymous):

so my answer would be 2?

OpenStudy (anonymous):

it gets me confused because it says round thats why

OpenStudy (whpalmer4):

Certainly not! How can a triangle have a hypotenuse that is shorter than one side?

OpenStudy (whpalmer4):

in my drawing, \(c\) is the distance between the two points, right?

OpenStudy (anonymous):

yeah

OpenStudy (whpalmer4):

|dw:1393631483304:dw| Sorry, I guess I didn't label the other point, but it should have been evident from the scale markings

OpenStudy (whpalmer4):

So, \(a\) is the difference in the \(x\) values, or \((x_2-x_1)\) \(b\) is the difference in the \(y\) values, or \((y_2-y_1)\) \(c\) is the hypotenuse of the right triangle with legs \(a, b\), so \[c=\sqrt{a^2+b^2}\]

OpenStudy (whpalmer4):

Because one of your points is the origin, the equation is in simpler form than usual, because the difference in the x values is just the x coordinate of the other point, and the difference in the y values is just the y coordinate of the other point. Both of them get squared before taking the square root, so it doesn't matter which point is which, because we always get a positive number when squaring a real number.

OpenStudy (anonymous):

im sorry im just very lost

OpenStudy (whpalmer4):

Tell me the first thing that you don't understand.

OpenStudy (anonymous):

what do i plug in the first formula you gave me?

OpenStudy (whpalmer4):

the coordinates of the two points! One is the origin, which by definition is (0,0). The other is the point (5,-2).

OpenStudy (whpalmer4):

basically, you're finding out how far the points are apart going along the x axis, and how far they are apart going along the y axis. Then you square both of those numbers, add them, and take the square root to get the straight line distance between them.

OpenStudy (anonymous):

5.39 is the answer

OpenStudy (whpalmer4):

Yes, that's correct. \(\sqrt{29}\approx 5.38516\)

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