calculate the coordinate of Point P3 given the following data

Question

I need to calculate the coordinate of Point P3 given the following data.

Distance D from P1 = 3
P1 coord = (1,3)
P2 coord = (10,6)

please help me to solve this issue..

i understand I have to use the distance formula between to coordinate.. but my math is very rusty can find the way to calculate the inverse formula.

$$D(P1-P3) = \sqrt{(P2x - P1x)^2 + (P2y - P1y)^2}$$

but... I don't know how to procede.. I need to calculate X,Y of point P3.

can someone show me what the step to take in order to get the coordinate of P3?

Thanks a lot

Answer 1

1. Use "2-point form" to get L, the equation of P1P2.

---> $L: \dfrac {y - 2}{x - 1} = \dfrac {6 - 2}{10 - 1}$

2. Form C, the equation of the circle (centered at P1 with radius = 3). $C: (x - 1)^2 + (y - 2)^2 = 3^3$

3. P3 is located at the intersection of L and C. Therefore, solve L and C to get P3. [Will get 2 sets of answers from the combined quadratic equation. Choose the one between P1 and P3.]