Question

The area of triangle is 5. Square unit two of its vertices are (2,1)( 3,-2 ) third vertices lies on the line y=X+3 find the third vertex

Answer 1

The third vertices of the triangle is (4,5)

Step-by-step explanation:

let the third vertex of the traingle be (x,y)

∵ the third vertyex (x,y) lies on the line $y=x+3$

∴ the third vertex will be (x,x+3)

Area of the triangle is 5 sq unit (given)

Also the area of triangle can be written as

$Area =\frac{1}{2} [x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]$

let x₁=x, x₂=2, x₃=3

   y₁=x+1, y₂=1, y₃=-2

on substituting these vaklues we get

$=>5=\frac{1}{2} [x(1+2)+2(-2-x-1)+3(x+1-1)]\\=>5=\frac{1}{2} (4x-6)\\=>5=2x-3\\=>x=4$

therefore the third vertex will be (4,4+1)

i,s. (4,5)