How do you find the distance between points (3,-3), (7,2)?

2 Answers
May 24, 2017

Answer:

#d=sqrt(41)#

Explanation:

Use the distance formula: #d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
If we let #(3,-3)->(color(blue)(x_1),color(red)(y_1))# and #(7,2)->(color(blue)(x_2),color(red)(y_2))# then...

#d=sqrt((color(blue)(7-3))^2+(color(red)(2--3))^2)#

#d=sqrt((color(blue)(4))^2+(color(red)(5))^2)#

#d=sqrt((color(blue)(16))+(color(red)(25))#

#d=sqrt(41)#

May 24, 2017

Answer:

The distance between points (3,-3), (7,2) is #d=sqrt41#

That is #approx6.4 units#

Explanation:

Use the distance formula which is derived from the Pythagorean Theorem.

They did it here:
http://www.purplemath.com/modules/distform.htm

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

We have points (3,-3), (7,2):

Then: #d^2 = (3-7)^2+(-3-2)^2#

#d^2 = (-4)^2+(-5)^2#

See how squaring gets rid of those nasty negatives?

#d^2 = (16)+(25)#

Too bad we cannot take the roots of the two terms without adding.

#d^2 = 41#

#d = sqrt41 approx 6.4#

To check, compare this #right angle triangle 4, 5, 6.4# to a standard #right angle triangle3, 4, 5#, and they appear to be similar.