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Answer 1 · 2017-10-11T03:16:15

The distance is #\sqrt{72}# units on the coordinate plane.

You can solve this using the Distance Formula, which is derived from the Pythagorean Theorem.

#d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}#

where #(x_1,y_1)# and #(x_2,y_2)# are two points.

In your question, we have:

#(x_1,y_1)=(-4,8)#

and

#(x_2,y_2)=(2,2)#

So, we can write the distance formula as:

#d=\sqrt{(2-(-4))^2+(2-8)^2}#

#d=\sqrt{(6)^2+(-6)^2}#

#d=\sqrt{36+36}#

#d=\sqrt{72}#

#\therefore# the distance between #(-4,8)# and #(2,2)# is #\sqrt{72}#

Answer 2 · 2017-10-11T10:24:30

See a solution process below:

The formula for calculating the distance between two points is:

#d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)#

Substituting the values from the points in the problem gives:

#d = sqrt((color(red)(2) - color(blue)(-4))^2 + (color(red)(2) - color(blue)(8))^2)#

#d = sqrt((color(red)(2) + color(blue)(4))^2 + (color(red)(2) - color(blue)(8))^2)#

#d = sqrt(6^2 + (-6)^2)#

#d = sqrt(36 + 36)#

#d = sqrt(36 * 2)#

#d = sqrt(36)sqrt(2)#

#d = 6sqrt(2)#