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The ends of the base of an isosceles right angled triangle are (1,2) (3,4).The possible positions for the vertex of the triangle are
- (2,3) (3,2)
- (1,4) (-3,-2)
- (1,4) (3,2)
- (3,2) (4,3)
- none

let the isoceles triangle be ABC.Therefore AB=AC (property)

then apply distance formula of AB &AC

then u will get the vertex of the triangle ABC.

Hope its useful!!!!