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

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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)   (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 to the midpoint of we need first to find the midpoint of

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 ,


Since the second point is (-2, 2), we can also say (x2, y2) = (-2, 2)
So ,


Put this all together to get: , , , and

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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 =


X Coordinate of Midpoint =


X Coordinate of Midpoint =


X Coordinate of Midpoint =



So the x coordinate of the midpoint is -1


----------------------------------------------------------------------------------------


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 =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


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 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 ,


Since the second point is (-1, 1), we can also say (x2, y2) = (-1, 1)
So ,


Put this all together to get: , , , and

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






Plug in , , , and
















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Answer:


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


The approximate distance between the two points is about 3.60555127546399 units



So again,


Exact Distance: units


Approximate Distance: units




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