What is the distance between #(8, 2) # and # (4, -5) #?

3 Answers
Dec 29, 2015

Answer:

#"Distance" = 8.06 " to 3 significant figures"#

Explanation:

#Deltax = 8 - 4 = 4#

#Deltay = 2 - (- 5) = 7#

#h^2 = Deltax^2 + Deltay^2#

#h = sqrt((Deltax^2 + Deltay^2))#

#h = sqrt((4^2 + 7^2))#

#h = sqrt((16 + 49))#

#h = sqrt(65)#

#h = 8.062257748#

#h = 8.06" to 3 significant figures"#

Dec 29, 2015

Answer:

#"line" ~=8.06 #

Explanation:

(8, 2) and (4, -5) are two points in a cartesian plane.enter image source here
The line represents the distance between the points. The size of the line can be calculated using Pythagoras' formula: #"line"^2 = "difference in x"^2 + "difference in y"^2 #:
#"line"^2 = 4^2 + 7^2#
#"line"^2 = 16 + 49#
#"line" = sqrt(65) #
#"line" ~=8.06 #

Dec 29, 2015

Answer:

#sqrt(65)#

Explanation:

The distance formula for Cartesian coordinates is

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2#
Where #x_1, y_1#, and#x_2, y_2# are the Cartesian coordinates of two points respectively.
Let #(x_1,y_1)# represent #(8,2)# and #(x_2,y_2)# represent #(4,-5)#.

#implies d=sqrt(((4-8))^2+(-5-2)^2)#
#implies d=sqrt((-4)^2+(-7)^2#
#implies d=sqrt(16+49)#
#implies d=sqrt(65)#
#implies d=sqrt(65)#

Hence the distance between the given points is #sqrt(65)#.