Question

The area of a triangle is 5. Two of the vertices are (2,1)and(3,-2)and third vertex lie on y=x+3. Find the third vertex.

Answer 1

Let ABC be a triangle with A(a,b),
B(2,1) and C(3,-2).
A lies on the line y=x+3 means..
b=a+3.....................(1).
Area of ∆ABC=(1/2)|a  b  1|
                                    |2  1  1|
                                    |3  -2 1|
=>5=(1/2)(3a+b-7)
=>3a+b=17.............(2)
Solving (1) and (2) for a and b we get
a=7/2 and b=13/2
Hence coordinates of the vertex A are
(7/2,13/2).
Hope it helps you to understand your problem......