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

Algebra ->  Linear-equations -> SOLUTION: for the points (1,4) and (-5,-1) find the distance and the midpoint.      Log On


   

Question 775986: for the points (1,4) and (-5,-1) find the distance and the midpoint.
Answer by MathLover1(20850) About Me  (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 x%5B1%5D+=+1, y%5B1%5D+=+4


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


Put this all together to get: x%5B1%5D+=+1, y%5B1%5D+=+4, x%5B2%5D+=+-5, and y%5B2%5D+=+-1

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


Now use the distance formula to find the distance between the two points (1, 4) and (-5, -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%281+-+%28-5%29%29%5E2+%2B+%284+-+%28-1%29%29%5E2%29 Plug in x%5B1%5D+=+1, y%5B1%5D+=+4, x%5B2%5D+=+-5, and y%5B2%5D+=+-1


d+=+sqrt%28%281+%2B+5%29%5E2+%2B+%284+%2B+1%29%5E2%29


d+=+sqrt%28%286%29%5E2+%2B+%285%29%5E2%29


d+=+sqrt%2836+%2B+25%29


d+=+sqrt%2861%29


d+=+7.81024967590665

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

Answer:


The distance between the two points (1, 4) and (-5, -1) is exactly sqrt%2861%29 units


The approximate distance between the two points is about 7.81024967590665 units



So again,


Exact Distance: sqrt%2861%29 units


Approximate Distance: 7.81024967590665 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 x%5B1%5D+=+1, y%5B1%5D+=+4


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


Put this all together to get: x%5B1%5D+=+1, y%5B1%5D+=+4, x%5B2%5D+=+-5, and y%5B2%5D+=+-1

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




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 = %281%2B-5%29%2F2


X Coordinate of Midpoint = -4%2F2


X Coordinate of Midpoint = -2



So the x coordinate of the midpoint is -2


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


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 = %284%2B-1%29%2F2


Y Coordinate of Midpoint = 3%2F2


Y Coordinate of Midpoint = 1.5


So the y coordinate of the midpoint is 1.5



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


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)