Zinot divu punktu A ( x 1 ; y 1 ) A(x_1;\ y_1) A ( x 1 ; y 1 ) B ( x 2 ; y 2 ) B(x_2;\ y_2) B ( x 2 ; y 2 ) A B ⃗ \vec{AB} A B
A ( x 1 ; y 1 ) A\;(x_{1}; y_{1}) A ( x 1 ; y 1 ) B ( x 2 ; y 2 ) B\;(x_{2}; y_{2}) B ( x 2 ; y 2 )
d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 d d d ( x 1 ; y 1 ) (x_1;\ y_1) ( x 1 ; y 1 ) ( x 2 ; y 2 ) (x_2;\ y_2) ( x 2 ; y 2 )
Doti punkti A ( 1 ; 3 ) A(1;\ 3) A ( 1 ; 3 ) B ( 4 ; 7 ) B(4;\ 7) B ( 4 ; 7 )
x 1 = 1 y 1 = 3 x 2 = 4 y 2 = 7 x_1 = 1\quad y_1 = 3\quad x_2 = 4\quad y_2 = 7 x 1 = 1 y 1 = 3 x 2 = 4 y 2 = 7
Ievietojam koordinātas formulā un vienkāršojam:
d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 = ( 4 − 1 ) 2 + ( 7 − 3 ) 2 = 3 2 + 4 2 = \sqrt{(4 - 1)^2 + (7 - 3)^2} = \sqrt{3^2 + 4^2} = ( 4 − 1 ) 2 + ( 7 − 3 ) 2 = 3 2 + 4 2 = 9 + 16 = 25 = 5 = \sqrt{9 + 16} = \sqrt{25} = {\color{#1865f2} 5} = 9 + 16 = 25 = 5 d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 = ( 4 − 1 ) 2 + ( 7 − 3 ) 2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(4 - 1)^2 + (7 - 3)^2} d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 = ( 4 − 1 ) 2 + ( 7 − 3 ) 2 = 3 2 + 4 2 = 9 + 16 = 25 = 5 = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = {\color{#1865f2} 5} = 3 2 + 4 2 = 9 + 16 = 25 = 5 