SOLUTION: Given the points (-5,6) and (7,1) find the length and slope of the segment that connects them.

Algebra ->  Linear-equations -> SOLUTION: Given the points (-5,6) and (7,1) find the length and slope of the segment that connects them.      Log On


   

Question 316757: Given the points (-5,6) and (7,1) find the length and slope of the segment that connects them.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: is the first point . So this means that x%5B1%5D=-5 and y%5B1%5D=6.
Also, is the second point . So this means that x%5B2%5D=7 and y%5B2%5D=1.


Length:


d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%28-5-7%29%5E2%2B%286-1%29%5E2%29 Plug in x%5B1%5D=-5, x%5B2%5D=7, y%5B1%5D=6, and y%5B2%5D=1.


d=sqrt%28%28-12%29%5E2%2B%286-1%29%5E2%29 Subtract 7 from -5 to get -12.


d=sqrt%28%28-12%29%5E2%2B%285%29%5E2%29 Subtract 1 from 6 to get 5.


d=sqrt%28144%2B%285%29%5E2%29 Square -12 to get 144.


d=sqrt%28144%2B25%29 Square 5 to get 25.


d=sqrt%28169%29 Add 144 to 25 to get 169.


d=13 Take the square root of 169 to get 13.


So our answer is d=13


So the distance between the two points is 13 units.


So this means that the line segment is 13 units long.



Slope:

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%281-6%29%2F%287--5%29 Plug in y%5B2%5D=1, y%5B1%5D=6, x%5B2%5D=7, and x%5B1%5D=-5


m=%28-5%29%2F%287--5%29 Subtract 6 from 1 to get -5


m=%28-5%29%2F%2812%29 Subtract -5 from 7 to get 12


So the slope of the line that goes through the points and is m=-5%2F12