What is the distance between #(15,-4)# and #(7,5)#?

2 Answers
Jun 27, 2017

Answer:

See a solution process below:

Explanation:

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)(7) - color(blue)(15))^2 + (color(red)(5) - color(blue)(-4))^2)#

#d = sqrt((color(red)(7) - color(blue)(15))^2 + (color(red)(5) + color(blue)(4))^2)#

#d = sqrt((-8)^2 + 9^2)#

#d = sqrt(64 + 81)#

#d = sqrt(145)#

Or

#d= 12.042# rounded to the nearest thousandth.

Jun 27, 2017

It might not seem like it, but this question just invooves simple Pythagorus on a graph. Instead of getting the two lengths of the known sides, it has to be worked out by finding the length.

However, this is super easy, just fin the change in #x# and the change in #y#.

To get from 15 #to# 7 we go back by 8, however, we are talking about length, so we take it as #abs(-8) = 8#, and not #-8#. Pur horizontal side has a length of 8.

To get from -4 #to# 5 we go up by 9. This will give us a verticle length of 9.

Now we have a right-angled triangle of lengths 8, 9, and #h#, #h# being the hypotenuse (longest side) of the triangle.

To find the length of #h#, we use #a^2 = b^2 + c^2#, where #a=sqrt(b^2+c^2)

We add our values in to get #h=sqrt(8^2+9^2)=sqrt(64+81)=sqrt(145)=12.0415946~~12.0#