Question

a straight line passing through the point P(1,2) and making an angle with the positive X axis 45 degree at the point Q and the value of PQ=3root2 then measure the coordinates of point Q

Answer 1

Answer:

Step-by-step explanation:

Method I

The intersection point lies on circles with diameter AB and AC since there is right angle at the foot of the perpendicular.

Equation of circle with diameter  AB  

(x−4)(x−1)+(y+3)(y−1)=0  

x2+y2–5x+2y+1=0(1)

Equation of circle with diameter  AC  

(x−4)(x−2)+(y+3)(y−3)=0  

x2+y2–6x−1=0(2)

Subtracting  (2)  from (1)  we get equation of common chord  AD  which is perpendicular to  BC  

x+2y+2=0  

Method II

Equation of  BC  

(x2−x1)(y−y1)−(y2−y1)(x−x1)  

(2–1)(y−1)−(3–1)(x−1)=0  

y−2x−1=0(3)

equation of perpendicular is obtained by exchanging the coefficients of x and y and changing sign of one of them.On R.H.S. put the values of point from which it passes.

x+2y=4–6=−2