The area of a triangle is 5 sq. units. Two of its vertices are (2,1)  and  (3,−2) . The third vertex lying on y=x+3.  The coordinates of the third vertex are given by

As the vertex lies on the line y=x+3  its coordinates are of the form (x,x+3),  The area of the triangle those vertices are (2,1),(3,−2)  and  (x,x+3),  is |12|2113−21xx+31||=12|4x−4|=|2x−2| Accordingly to the given coordinates 2x−2=±5 ⇒    x=−32,72 .Thus the coordinates of the third vertex can be (−32,32),(72,132) .