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
  1. ​(2,3) (3,2)
  2. (1,4) (-3,-2)
  3. (1,4) (3,2)
  4. (3,2) (4,3)
  5. none

if it is an MCQ then all u have to do is :
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!!!!
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