Question

The x coordinate of a point p is twice it's y-coordinate if p is equidistant from Q(2, -5) andr(-3, 6) find coordinate of p

Answer 1

Answer:

Step-by-step explanation:

Then, its x-coordinate will be 2a. Thus, the coordinates of the point P are (2a, a). t is given that the point P (2a, a) is equidistant from Q (2, −5) and R (−3, 6). Thus, the coordinates of the point P are (16, 8), i.e. (2 × 8, 8).

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)