Question 55427
Use the point slope formula to find the horizontal and vertical distances between the points
{{{m=(y[2]-y[1])/(x[2]-x[1])}}}m=slope
{{{m=(-7-(-4))/(-5-(-1))}}}Plug in x and y values of the points
{{{m=(3)/(4)}}}Simplify
Since the slope is 3/4, it really means between the points (-1, -4) and (-5, -7) the vertical distance ("rise") is 3 and the horizontal distance ("run") is 4. However, we want the diagonal distance between the points, which happens to be the hypotenuse of the vertical and horizontal lengths. So to find the hypotenuse we use Pythagoreans theorem to find it
{{{a^2+b^2=c^2}}}Pythagoreans theorem: in this case a and b are known lengths and c is the hypotenuse
{{{3^2+4^2=c^2}}}Plug in known points
{{{9+16=c^2}}}Simplify   
{{{25=c^2}}}
{{{sqrt(25)=sqrt(c^2)}}}isolate c by taking square root of both sides
{{{c=5}}}
So distance between the two points is 5 units