SOLUTION: Find All points having an x-coordinate of 9 distance from the point is (3,-2) is 10

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Question 1135669: Find All points having an x-coordinate of 9 distance from the point is (3,-2) is 10
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
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Find All points having an x-coordinate of 9 distance from the point is (3,-2) is 10
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Unclear.

Read your post and try to understand what is written there.



Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
?

Distance from point (3,-2) is 10:
%28x-3%29%5E2%2B%28y%2B2%29%5E2=100



All points having x coordinate of 9:
y%2B2=sqrt%28100-%28x-3%29%5E2%29
y=-2%2Bsqrt%28100-%28x-3%29%5E2%29
letx=9.
y=-2%2Bsqrt%28100-36%29
y=-2%2Bsqrt%2864%29
y=-2%2B-+8
system%28y=-10%2Cor%2Cy=6%29
check to see if either of these fail.

Answer by greenestamps(13196) About Me  (Show Source):
You can put this solution on YOUR website!


Taking just a LITTLE more time when submitting your post to make it clear would be a good thing to do....

You wrote: "Find All points having an x-coordinate of 9 distance from the point is (3,-2) is 10"

Try, perhaps: "Find all points having an x-coordinate of 9, if the distance from the point (3,-2) is 10"

You want the distance from (3,2) to (9,y) to be 10.

You can use the distance formula (aka the Pythagorean Theorem) to solve the problem; but it's not needed.

The difference in the x coordinates is 6 and the distance is 10; that means you have a right triangle with one leg 6 and hypotenuse 10. That makes the other leg 8. (it is a multiple of the simplest Pythagorean triple, 3-4-5).

So the two y values are 8 more or less than the y value of the given point.

(1) 2+8 = 10
(2) 2-8 = -6

ANSWERS: (9,10) and (9,-6)