Lots of points for best answer!

c=a^2+b^2

c =√(x2-x1)2 + (y2-y1)2)

substitute it value

points G and I have coordinates (6,4) and (3,2)

To Find : Use  Pythagorean theorem  to calculate the straight line distance between points G and I

Solution:

points G and I have coordinates (6,4) and (3,2)

Draw a line parallel to y axis passing through G

Draw a line parallel to x axis passing through I

Intersection point K ( 6 , 2)

IK = 6 - 3 = 3

GK = 4 -2  = 2

ΔIKG right angled triangle

Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.  

GI² = IK² + GK²

=>  GI²  = 3² + 2²

=>  GI²  = 13

=> GI = √13

using distance formula

G (6,4) and I (3,2)

= √(6 - 3)² + (4 - 2)²

= √3² + 2²

= √9 + 4

= √13