What is the distance between # (2, 5) # and # (–7, 8) #?

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Answer 1 · 2015-12-07T15:51:13

#d~~9.49# to 2 decimal places

#d= 3sqrt(10)color(white)(....)color(blue)("exactly!")#

Tony B

Let the distance between be d

Let #(x_1,y_1) -> (2,5)#
Let #(x_2,y_2)-> (-7,8)#

#color(brown)("Using Pythagoras:")#

#d^2 = ("difference in x")^2 +("difference in y")^2#

#d^2 = (x_2 - x_1)^2+(y_2 -y_1)^2#

#d^2 = (-7-2)^2+(8-5)^2#

#d^2 = (-9)^2+(3)^2#

#d^2= 81+9 = 90#

#d=sqrt(90)#

#d~~9.49# to 2 decimal places
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

More accurately

#d=sqrt(9xx10)#

#d=sqrt(3^2xx10)#

#d= 3sqrt(10)color(white)(....)color(blue)("exactly!")#