Question

The x-coordinate of q point p is twice its y-coordinate.If p is equidistance from q(2,-5)and r(-3,6) find the coordinate of p.

Answer 1

Let P(x,y) is the required point

.Let Q(2,−5) and R(−3,6) are the given points.

Now, PQ = PR

⇒PQ2 = PR2  

 ⇒(x−2)2+(y+5)2 = (x+3)2+(y−6)2     

[Using distance formula]

⇒x2+4−4x+y2+25+10y = x2+9+6x+y2+36−12y

⇒−4x+10y+29 = 6x−12y+45

⇒−10x+22y−16 = 0

⇒−10(2y) + 22y = 16

=2y =16

=) y =8

now x=2y = 2 × 8 = 16

So coordinates of required point

P are P(16,8)