For us to determine the distance between two points on the Cartesian plane we need to use the Pythagorean Theorem which is:
[tex]a^2+b^2=c^2[/tex]
We let the coordinates as follows:
For point A: [tex](x_a,y_a)=(-3,0)[/tex]
For point B: [tex](x_b,y_b)=(7,1)[/tex]
The Pythagorean Theorem would be:
[tex](x_a-y_a)^2+(x_b-y_b)^2=c^2[/tex]
We substitute the values:
[tex]c^2=(-3-7)^2+(0-1)^2
=(-10)^2+(-1)^2
=100+1
=101[/tex]
The value of c is the square root of 101 which is either [tex] \sqrt{101} [/tex] or [tex]- \sqrt{101} [/tex] but since the distance between two points can never be negative then the distance between A and B is [tex] \sqrt{101} [/tex]
