SOLUTION: for the points (1,4) and (-5,-1) find the distance and the midpoint.

Algebra.Com
Question 775986: for the points (1,4) and (-5,-1) find the distance and the midpoint.
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

the distance:
Solved by pluggable solver: Distance Formula


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


Since the first point is (1, 4), we can say (x1, y1) = (1, 4)
So ,


Since the second point is (-5, -1), we can also say (x2, y2) = (-5, -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 (1, 4) and (-5, -1)






Plug in , , , and
















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Answer:


The distance between the two points (1, 4) and (-5, -1) is exactly units


The approximate distance between the two points is about 7.81024967590665 units



So again,


Exact Distance: units


Approximate Distance: units





the midpoint:
Solved by pluggable solver: Midpoint


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


Since the first point is (1, 4), we can say (x1, y1) = (1, 4)
So ,


Since the second point is (-5, -1), we can also say (x2, y2) = (-5, -1)
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 -2


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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 =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


So the y coordinate of the midpoint is 1.5



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Summary:


The midpoint of the segment joining the two points (1, 4) and (-5, -1) is (-2, 1.5).


So the answer is (-2, 1.5)



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