Consider the two points P1=(-2,4) and P2=(3,-2) in the xy plane.Find the distance D between P1 and P2Find the midpoint M between P1 and P2Write an equation of the circle centered at the midpoint M you found in the previous question and whose radius is so that the points P1 and P2 are on the circle.

Question
Asked Oct 8, 2019
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Consider the two points P1=(-2,4) and P2=(3,-2) in the xy plane.

Find the distance D between Pand P2

Find the midpoint M between P1 and P2

Write an equation of the circle centered at the midpoint M you found in the previous question and whose radius is so that the points Pand Pare on the circle.

check_circle

Expert Answer

Step 1
Given that two points P (-2,4) and P (3,-2) lies in xy plane
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Given that two points P (-2,4) and P (3,-2) lies in xy plane

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Step 2

Find the distance D between P1 and P2 as follows.

D (x-x)(y-y
(3-(-2)+(-2-4)
(3+2)* +(-6)*
2
= 25+36
= V61
= 7.8
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D (x-x)(y-y (3-(-2)+(-2-4) (3+2)* +(-6)* 2 = 25+36 = V61 = 7.8

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Step 3

Now find the midpoint M between P1 and ...

M +x + y2
2
2
-2+3 4+(-2)
2
2
1 2
2 2
=(0.5,1)
The radius of the circle is
3.9
2
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M +x + y2 2 2 -2+3 4+(-2) 2 2 1 2 2 2 =(0.5,1) The radius of the circle is 3.9 2

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