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Question: Find the distance between the following pairs of point (-5, 7)(-1,3)....

Find the distance between the following pairs of point (-5, 7)(-1,3).

Explanation

Solution

Hint:Let us assume the distance between the above points as A(-5, 7) B(-1,3) as AB. Using the distance between two formula i.e AB=(x2−x1)2+(y2−y1)2AB= \sqrt {{{({x_2} - {x_1})}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} simplify it and get the required answer.

Complete step-by-step answer:
Now Let two given points be A(-5, 7) and B(-1, 3)
Thus, we have
x1=−5{x_1} = - 5 and x2=−1{x_2} = - 1
y2=7{y_2} = 7 and y1=3{y_1} = 3
The distance between two points is given as,
AB=(x2−x1)2+(y2−y1)2AB = \sqrt {{{({x_2} - {x_1})}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}}
AB=(−1+5)2+(3−7)2(Substituting the above values)AB = \sqrt {{{( - 1 + 5)}^2} + {{(3 - 7)}^2}} {(\text{Substituting the above values})}
=(4)2+(−4)2=16+16= \sqrt {{{(4)}^2} + {{( - 4)}^2}} = \sqrt {16 + 16}
=42units= 4\sqrt 2 units
Hence, the distance between the points would be 42units4\sqrt 2 units .

Note: As in the above question we used the basic formula of finding the distance between the two following pairs of the given points. First we assume the distance between them to be AB then by placing the formula and solving the equation we the distance between the two points.To find exact value simplify the solution further and find the value of of 2\sqrt2 by using division method and multiply with 4 we get distance between two points.