Since we want point A to be as close to the origin as possible, let point A lie on the x axis and its coordinates be (a,0) The distance of A from side BC (lying on the line x=4 ) is the height of the triangle ⇒ The height of the triangle ABC=|a−4| Given the area of the triangle =32
⇒(1/2)×8×|a−4|=32⇒|a−4|=8
⇒a=12 or -4 Required answer is the shortest distance from (0,0) i.e. 4 when a=−4.