What is the distance between the points (-4,2) and (3,-5)

7√2 units

Step-by-step explanation:

The distance between two points having coordinates (x1, y1) and (x2, y2) is given by,

Here, x1=-4 and y1=2

x2=3 and y2=-5

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

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step-by-step explanation: