Question

ABC is an isosceles triangle whose base is BC.if B and C are ( a+b , b-a ) and (a-b , a+b) then the coordination of A may be

Answer 1

Solution:

As, ABC is an isosceles triangle whose base is BC.if B and C are ( a+b , b-a ) and (a-b , a+b).

So, AB=AC

Let coordinates of A be (h,k).

Distance between two points is given by the formula:

$\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2$

AB²= AC²

→[h-(a+b)]²+[k-(b-a)]²=[h-(a-b)]²+[k-(a+b)]²

→h²+ (a+b)²-2 h (a+b)+k²+(b-a)²-2 k(b-a)=h²+ (a-b)²-2 h (a-b)+k²+(b+a)²-2 k(b+a)

Cancelling , h², k², (a+b)², (a-b)² from both sides

→h(a+b)+k(b-a)=h(a-b)+k(a+b)

→ h a + h b+ k b- k a= ha - h b + k a + k b

→cancelling h a and k b from both sides, gives

2 h b= 2 k a

h b= k a

$\frac{a}{b}=\frac{h}{k}\\\\ \frac{h}{a}=\frac{k}{b}=m\\\\ h= am, k=bm$

So, coordinate of A=(h,k)=(Multiple of a, Multiple of b)=(a m, b m)