Question 596072: A circle has its center at(4,0) and a radius of 5 units. Which quadrants does the circle pass through.
Found 2 solutions by Alan3354, math-vortex:
Answer by Alan3354(69443)   (Show Source):
Answer by math-vortex(648)  (Show Source):
You can put this solution on YOUR website! Hi, there--
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This circle passes through all four quadrants. Here's why:
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[I] Quadrant I
The center of this circle is at (4,0) on the x-axis. Since the radius is 5 units, every point on the circle is exactly 5 units from (4,0). The point (4,5) is 5 units directly above (4,0). We can see that (4,5) is in quadrant I because the x- and y-coordinates are both positive.
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{II}Quadrant IV
Using similar reasoning, the point (4,-5) is 5 units directly below (4,0). We can see that (4,-5) is in Quadrant IV because the x-coordinate is positive, and the y-coordinate is negative.
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[III] Quadrant II
We can use the distance formula to show that the circle passes through these quadrants. The point (-1,0) is 5 units directly to the left of (4,0). Let's choose an x-coordinate between 0 and -1, say -0.5. We'll use the distance formula to find the y-coordinate of the point that is exactly 5 units from the center, (4,0).
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Now, solve for y. Square both sides of the equation.
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The square root of 5.64 is a positive number, about 2.4. We know that the point (-0.5, sqrt(5.64)) is in Quadrant II because the x- and y-coordinates are positive, negative, respectively.
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Quadrant III
The point (-0.5,-sqrt(5.64)) is also exactly 5 units from (4,0). Try it in the distance formula above to see that this is the case. This point is in Quadrant III because both coordinates are negative.
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Hope this helps! Feel free to email if you have questions about the explanation.
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Ms.Figgy
math.in.the.vortex@gmail.com
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