Question

The extremities of the base of an isosceles triangle are $(2,0)$ and $(0,2)$. If the equation of one of the equal sides is $x=2$, then equation of other equal side is

• A. $x+y=2$
• B. $x-y+2=0$
• C. $y=2$
• D. $2x+y=2$

Answer 1

The correct option is C $y=2$

Equation of the base will be

$x+y=2$...(i)

Now the altitude from the vertex opposite to the base will bisect the base. Hence the altitude will pass through the mid point of $(2,0)$ and $(0,2)$ and will be perpendicular to $x+y=2$.

Thus the equation of the altitude will be $x-y=d$

It passes through the midpoint of the base, $(1,1)$.

Hence the equation of altitude is

$y=x$.

Hence the third vertex will be of the form $(x,x)$.

Since $x=2$ is one of the side, hence the third vertex will be $(2,2)$.

Thus another side will be $y=2$.