SOLUTION: given points A(0,0), B(2,-1) and C(-2,2), find the distance from B to the midpoint of AC. A)square root 13 B)13 C)square root 10 D)3 couldnt find the square root symbole s

Algebra ->  Testmodule -> SOLUTION: given points A(0,0), B(2,-1) and C(-2,2), find the distance from B to the midpoint of AC. A)square root 13 B)13 C)square root 10 D)3 couldnt find the square root symbole s      Log On


   

Question 911628: given points A(0,0), B(2,-1) and C(-2,2), find the distance from B to the midpoint of AC.
A)square root 13
B)13
C)square root 10
D)3
couldnt find the square root symbole so i type the squre root

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given points A(0,0), B(2,-1) and C(-2,2),


to find the distance from B+ to the midpoint of AC we need first to find the midpoint of AC

Solved by pluggable solver: Midpoint


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (0, 0), we can say (x1, y1) = (0, 0)
So x%5B1%5D+=+0, y%5B1%5D+=+0


Since the second point is (-2, 2), we can also say (x2, y2) = (-2, 2)
So x%5B2%5D+=+-2, y%5B2%5D+=+2


Put this all together to get: x%5B1%5D+=+0, y%5B1%5D+=+0, x%5B2%5D+=+-2, and y%5B2%5D+=+2

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Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2


X Coordinate of Midpoint = %28x%5B1%5D%2Bx%5B2%5D%29%2F2


X Coordinate of Midpoint = %280%2B-2%29%2F2


X Coordinate of Midpoint = -2%2F2


X Coordinate of Midpoint = -1



So the x coordinate of the midpoint is -1


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Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2


Y Coordinate of Midpoint = %28y%5B1%5D%2By%5B2%5D%29%2F2


Y Coordinate of Midpoint = %280%2B2%29%2F2


Y Coordinate of Midpoint = 2%2F2


Y Coordinate of Midpoint = 1


So the y coordinate of the midpoint is 1



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Summary:


The midpoint of the segment joining the two points (0, 0) and (-2, 2) is (-1, 1).


So the answer is (-1, 1)






now find the distance from B+ to the midpoint

Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (2, -1), we can say (x1, y1) = (2, -1)
So x%5B1%5D+=+2, y%5B1%5D+=+-1


Since the second point is (-1, 1), we can also say (x2, y2) = (-1, 1)
So x%5B2%5D+=+-1, y%5B2%5D+=+1


Put this all together to get: x%5B1%5D+=+2, y%5B1%5D+=+-1, x%5B2%5D+=+-1, and y%5B2%5D+=+1

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Now use the distance formula to find the distance between the two points (2, -1) and (-1, 1)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%282+-+%28-1%29%29%5E2+%2B+%28-1+-+1%29%5E2%29 Plug in x%5B1%5D+=+2, y%5B1%5D+=+-1, x%5B2%5D+=+-1, and y%5B2%5D+=+1


d+=+sqrt%28%282+%2B+1%29%5E2+%2B+%28-1+-+1%29%5E2%29


d+=+sqrt%28%283%29%5E2+%2B+%28-2%29%5E2%29


d+=+sqrt%289+%2B+4%29


d+=+sqrt%2813%29


d+=+3.60555127546399

==========================================================

Answer:


The distance between the two points (2, -1) and (-1, 1) is exactly sqrt%2813%29 units


The approximate distance between the two points is about 3.60555127546399 units



So again,


Exact Distance: sqrt%2813%29 units


Approximate Distance: 3.60555127546399 units