In geometry, some figures have common vertices. Mostly the geometric figures are without common vertices. If a triangle, quadrilateral and some geometric figures in a graph are lying without common vertices are refered same. In graph there are four quadrants in that some vertices are fall on common vertices, with out common vertices points of are plotted.
Geometric figure without common vertices
Without common vertices find the distance of two points
In geometry the triangle has three vertices; the vertices are not common vertices. The common vertices are formed only if two triangles are in same point without three common vertices. The distance between two un common vertices are find out by using the coordinates of the vertices (x1,x2) and (x2,x2) of the vertices.
Distance between two vertices = √(x2-x1)2 +(y2-y1)2
If the geometry figure having the common vertices in a graph
Examples for without common vertices
Distance of a vertices are find using distance formula:
Examples for distance between two vertices:
Ex 1: Find the distance formed by without common vertices, Vertices A(4,5), B(7,4)
Sol : Distance AB = √(x2-x1)2 +(y2-y1)2
X1=4 X2=7 Y1=5 Y2=4
AB = √(7-4)2+(4-5)2
= √(3)2+ (-1)2
= √9+1
= √10 units
Ex 2 : Find the distance formed by without common vertices, Vertices A(3,2), B(5,4)
Sol : Distance AB = √(x2-x1)2 +(y2-y1)2
X1=3 X2=5 Y1=2 Y2=4
AB = √(5-3)2+(4-2)2
= √(2)2+ (2)2
= √4+4
= √8 units
Ex 3 : Find the distance formed by without common vertices, Vertices A(6,4), B(10,8)
Sol : Distance AB = √(x2-x1)2 +(y2-y1)2
X1=6 X2=10 Y1=4 Y2=8
AB = √(10-6)2+(8-4)2
= √(4)2+ (4)2
= √16+16
= √32 units
Ex 4: Find the distance formed by without common vertices, Vertices A(3,3), B(4,8)
Sol : Distance AB = √(x2-x1)2 +(y2-y1)2
X1=3 X2=4 Y1=3 Y2=8
AB = √(4-3)2+(8-3)2
= √(1)2+ (5)2
= √1+25
= √26 units
Practice problems:
Q 1 Find the distance of two vertices A(1,1) B(1,2) Answer: √1 units
Q 2 Find the distance of two vertices A(2,2) B(1,1) Answer: √2 units
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