how to solve this. The area of the triangle is 5 sq.units,Two of its vertices are (2,1)and (3,-2).T he third vertix lies on y =x+3.Find the third vertex

  • 0

 Take the coordinates of third vertex as ( x,y) 

Using area of triangle formula,

1/2 ( x1 ( y2 - y3) + x2 ( y3 - y1 ) + x3 ( y1 - y2  ) ) = 5

1/2 ( 2 ( -2 -y  ) + 3 ( y - 1 ) + x ( ( 1+2)) = 5

Substituiting y = x+3

1/2 ( -4 -2( x + 3 ) + 3 ( x + 3 ) - 1 + 3x ) = 5

1/2 ( -4 - 2x - 6 + 3x + 9 - 1 +3x) = 5

1/2( -2 + 4x) = 5

-1 + 2x = 5

2x = 6

x = 3

y = 3+3 = 6

coordinates of third vertex are ( 3,6)

  • 1
What are you looking for?