Machelle P.

asked • 01/26/14

Find the distance p1= [-1,3] p2=[4,4]

Find the distanced (P1P2) between the given points p1 and p2
p1 (-1,3)
P2=(4,4)

Curt J.

Okay, so the distance formula:
d=√[(x2-x1)2+(y2-y1)2]
 
derives from the Pythagorean Theorem, which we use to determine the lengths of the sides of a right triangle:
A2+B2=C2
 
When you're asked a distance problem for two points like above, you can plot those points on a graph and draw a line between them (C).  I recommend actually drawing the graph so you can see what I mean.  This line is your distance (the shortest distance between two points, right? :-) )
 
Now, take the highest point and draw a vertical line down from it, then take the lowest point and draw a horizontal line across.  You've just drawn a right triangle.  So, if we determine the length of the horizontal side (A) and the length of the vertical side (B), we can determine the length of the final side (C) AKA the hypotenuse.
 
So the length of A is just the difference between the two x values in the points given (x2-x1).  The length of B is the difference between the two y values (y2-y1).
 
So, inserting these values into the Pythagorean Theorem, we get:
A2+B2=C2
(x2-x1)2+(y2-y1)2=C2
 
Taking the square root of both sides, we get:
√[(x2-x1)2+(y2-y1)2]=C
 
Which is our distance equation.  So as you can see, it all comes back to Pythagoras and his pesky triangles :-)
Report

01/26/14

3 Answers By Expert Tutors

By:

Vivian L. answered • 01/26/14

Tutor
3 (1)

Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACH

See tutors like this
See tutors like this
Hi Machelle;
p1= [-1,3] p2=[4,4]
This is a triangle.
One side of the triangle is the distance between the values of y...
y-y1
4-3=1
Another side of the triangle is the distance between the values of x...
x-x1
4--1
Subtracting a negative number is the same as adding a positive number...
4+1=5
Pythagorean  Theorem...
a2+b2=c2
a and b are the sides of established lengths 1 and 5.
c is the hypotenuse.  This is the length were are looking for.
12+52=c2
1+25=c2
26=c2
√26=c
 
Upvote • 0 Downvote
More
Report

Curt J. answered • 01/26/14

Tutor
5 (8)

Math/Science/General Ed Tutor in West Honolulu

See tutors like this
See tutors like this
Hi Machelle,
This problem utilizes what is known as the distance formula:
d=√[(x2-x1)2+(y2-y1)2]
 
Where p1=(x1,y1) and p2=(x2,y2)
Using this info, you should be able to solve.  Give me a moment and I can provide a more detailed explanation for WHY this distance formula works.
Upvote • 0 Downvote
More
Report

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.