Please check the picture to understand the solution better.
The Pythagorean Theorem which applies to right triangles states that:
[tex]a^2+b^2=c^2[/tex]
a and b are the lengths of the legs while c is the length of the hypotenuse.
In the Cartesian plane they are:
[tex]x_a-x_b=a[/tex]
[tex]y_a-y_b=b[/tex]
The points are have coordinates [tex](x,y)[/tex]
This means
[tex](x_a,y_a)[/tex] are the coordinates of the first point
and [tex](x_b,y_b)[/tex] are the coordinates of the second
So in the problem:
[tex](x_a,y_a)=(2,-2)[/tex] which are the coordinates of P
[tex](x_b,y_b)=(-1,2)[/tex] which are the coordinates of P
We substitute this to the Pythagorean theorem
[tex](2-(-1))^2+(-2-2)^2=c^2[/tex]
[tex]3^2+(-4)^2=c^2[/tex]
[tex]9+16=c^2 \\ 25=c^2 \\ 5=c[/tex]
The triangle that will be formed has a very common Pythagorean triple which is (3,4,5).
The length of the hypotenuse (or any length of a side) cannot be less than or equal to 0 so it cannot be -5.
Therefore the length of the line segment when you connect the two points is 5.
