Question

the area of a triangle is 5 square units .two of its vertices are (2,1) and (3,-2). the third vertex is (x,y) where y=x+3. find the coordinates of the third vertex

Answer 1

Let the third vertex A of the triangle lies on the line y = x + 3

So, coordinate of the third vertex = (h, h + 3)

Given, area of the triangle ABC = 5

=> (1/2)*|h(1 + 2) + 2(-2 - h - 3) + 3(h + 3 -1)| = 5

=> |3h - 2(-5 - h) + 3(h + 2)| = 5*2

=> |3h - 10 - 2h + 3h + 6| = 10

=> |4h - 4| = 10

=> 4h - 4 = ±10

=> 4h - 4 = 10 or 4h - 4 = -10

=> 4h = 10 + 4 or 4h = -10 + 4

=> 4h = 14 or 4h = -6

=> h = 14/4, -6/4

=> h = 7/2, -3/2

1. when h = 3/2, then

h + 3 = 7/2 + 3 = (7 + 6)/2 = 13/2

2. when h = -3/2, then

h + 3 = -3/2 + 3 = (-3 + 6)/2 = 3/2

So, the third coordinate of the vertex of the triangle are (7/2, 13/2) or (-3/2, 3/2)

Answer 2

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