What is the distance between (8, -3) and (4, -7)?

2 Answers
Jim G.
Mar 25, 2018

#4sqrt2~~5.66" to 2 dec. places"#

Explanation:

#"calculate the distance using the "color(blue)"distance formula"#

#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(8,-3)" and "(x_2,y_2)=(4,-7)#

#d=sqrt((4-8)^2+(-7+3)^2)#

#color(white)(d)=sqrt(16+16)=sqrt32=4sqrt2~~5.66#

NJ
Mar 25, 2018

#=> d = 4sqrt(2)#

Explanation:

In 2D cartesian coordinates, distance between two points is given as:

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

So for our problem:

#=> d = sqrt((4-8)^2 + (-7-(-3))^2)#

#=>d=sqrt((-4)^2 + (-4)^2)#

#=> d = sqrt(16+16)#

#=> d=sqrt(32)#

Now we can simplify by trying to find the largest square number we can pull out of the square root.

#=> d = sqrt(2xx16)#

#=> d = sqrt(2 xx 4^2)#

#=> d = 4sqrt(2)#

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