Considering the definition of distance, the distance between the pair of points (5,9) and (-7,-7) is 20 (second option).
Definition of distance
The distance between two points is equal to the length of the segment that joins them.
To determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of these squares. That is, the distance is the square root of the sum of the squares of the difference of the coordinates of the points (x1, y1) and (x2, y2):
distance=[tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} }[/tex]
The distance value always gives a positive sign value, because distances are always positive.
Distance in this case
In this case, you know:
- (x1,y1)= (5,9)
- (x2,y2)= (-7,-7)
So, the distance can be calculated as:
distance=[tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} }[/tex]
distance=[tex]\sqrt{(-7-9)^{2} +(-7-5)^{2} }[/tex]
Solving:
distance= [tex]\sqrt{(-16)^{2} +(-12)^{2} }[/tex]
distance= [tex]\sqrt{256 +144 }[/tex]
distance= [tex]\sqrt{400 }[/tex]
distance= 20
Finally, the distance between the pair of points (5,9) and (-7,-7) is 20 (second option).
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