Question

Two vertices of a triangle are (2,4) and (-2,3) and the area is 2 square units the locus of the third vertex is

• A. 4x - y = 14
• B. 4x + 4y = 14
• C. x + 4y = 12
• D. x - 4y = -14

Answer 1

The correct option is D x - 4y = -14

Let the third vertex be $A(x,y)$

The gIven vertices of the triangle are $B(2,4),C(-2,3)$

Area of the triangle =$2$

$2=\frac{|Ax(By-Cy)+Bx(Cy-Ay)+Cx(Ay-By)|}{2}$

$=>2=\frac{|x(4-3)+2(3-y)+(-2)(y-4))|}{2}$

$=>2=\frac{|x+6-2y-2y+8|}{2}$

$=>2=\frac{|x+14-4y|}{2}$

$=x-4y=-14$