What is the distance between (-3, -11) and (8, -42)

Please help I will give points

ca 32.89

Step-by-step explanation:

Firstly we need to know how far it is between the two points in both directions

In the x direction the distance is 8 - (-3) = 11

In the y-direction the distance is -42 -(-11) = -31

Then to find the shortest distance between the two points find the hypotenuse of the triangle we just made

31^2 + 11^2 = h^2

961 + 121 = h^2

1082 = h^2

h = ca 32.89

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4