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Distance entre deux points

Suivant les pays les notations sont différentes. Nous utilisons AB pour désigner la longueur du segment [AB]. Peut-être utilisez-vous |AB|.
Quels que soient A(x1,y1) et B(x2,y2) la distance entre A et B, c'est-à-dire la longueur du segment [AB] est :
AB=(x2x1)2+(y2y1)2
D'où vient cette formule et comment l'appliquer ?

Comprendre la formule

On place les points de coordonnées (x1 ;y1) et (x2 ;y2).
The first quadrant of a coordinate plane with two tick marks on the x axis labeled x one and x two. There are two tick marks on the y axis labeled y one and y two. There is a point at x one, y one and another point at x two, y two.
Il s'agit de calculer la distance entre ces deux points, c'es-à-dire la longueur du segment tracé en bleu.
The first quadrant of a coordinate plane with two tick marks on the x axis labeled x one and x two. There are two tick marks on the y axis labeled y one and y two. There is a point at x one, y one and another point at x two, y two. A line connects the two points.
Pour calculer cette longueur, on trace un triangle rectangle ce qui permettra d'utiliser le théorème de Pythagore.
The first quadrant of a coordinate plane with two tick marks on the x axis labeled x one and x two. There are two tick marks on the y axis labeled y one and y two. There is a point at x one, y one and another point at x two, y two. A line connects the two points. A third unlabeled point is at x two, y one with a line connecting from it to the point at x two, y two and another line connecting from it to the point at x one, y one forming a right triangle.
La longueur du côté de l'angle droit tracée en vert est x2x1:
The first quadrant of a coordinate plane with two tick marks on the x axis labeled x one and x two. There are two tick marks on the y axis labeled y one and y two. There is a point at x one, y one and another point at x two, y two. A line connects the two points. A third unlabeled point is at x two, y one with a line connecting from it to the point at x two, y two and another line connecting from it to the point at x one, y one forming a right triangle. The hypotenuse of the right triangle is unknown and the side made from the point at x one, y one and x two, y one is labeled x two minus x one.
De même, la longueur de l'autre côté de l'angle droit est y2y1 :
The first quadrant of a coordinate plane with two tick marks on the x axis labeled x one and x two. There are two tick marks on the y axis labeled y one and y two. There is a point at x one, y one and another point at x two, y two. A line connects the two points. A third unlabeled point is at x two, y one with a line connecting from it to the point at x two, y two and another line connecting from it to the point at x one, y one forming a right triangle. The hypotenuse of the right triangle is unknown and the side made from the point at x one, y one and x two, y one is labeled x two minus x one. The third side is labeled y two minus y one.
On utilise le théorème de Pythagore :
?2=(x2x1)2+(y2y1)2
La distance cherchée est :
?=(x2x1)2+(y2y1)2
On obtient la formule de la distance entre deux points de coordonnées données.
Si vous n'arrivez pas à mémoriser cette formule, il est toujours possible de tracer un triangle rectangle dont l'hypoténuse est le segment en question et d'appliquer le théorème de Pythagore.

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