Question

find the locus of the vertex A of an isosceles triangle whose base is the line joining the points B(2,-3) and C(-3,0)

Answer 1

let point A is ( P , Q)

according to property of isosceles ∆ we know , two sides length are equal .

e.g AB = AC

so, AB² = AC²

{( P-2)² + (Q +3)² } = { (P+3)² + Q² }

P² + 4 -4P + Q² + 9 +6Q = P² +6P + 9 +Q²

4 - 4P + 6Q = 6P

6P + 4P - 6Q = 4

10P - 6Q = 4

5P -3Q = 2

put P and Q are x and y respectively

5x - 3y =2

so, locus of point A is 5x -3y =2

Answer 2

using coordinate geometry....and some concepts of slope we can solve easily...

see attachment...

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hope it will help u