In order to know the distance between two points we have to perform the Pythagorean Theorem which is:
[tex]a^2+b^2=c^2[/tex]
Where a and b are the legs of the triangle and c is the hypotenuse (the longest side). Take note that this theorem only works on right triangles. We use this theorem since the distance between two points is the altitude of the hypotenuse.
Since we are given two points we let the coordinates be as follows:
[tex](x_a,y_a)=(1,3) \\ (x_b,y_b)=(-5,-5)[/tex]
The Pythagorean Theorem in the Cartesian plane is :
[tex](x_a-x_b)^2+(y_a-y_b)^2=c^2[/tex]
Without loss of Generality (WLOG) we let the leg a's altitude be the horizontal length and leg b's be the vertical length. Substituting the values we get:
[tex]c^2=(1-(-5))^2+(3-(-5))^2 \\ =6^2+8^2 \\ =36+64 \\ =100[/tex]
The altitude of c would be the square root of 100 which is either positive 10 or negative 10 so since the distance between two points can never be negative their distance is 10.
