A ray of light passing through the point \(P(1, 2)\) reflects on the \(x\)-axis at point \(N\) and the reflected ray passes through the point \(Q(5, 3)\). What is the distance of the point \(N\) from the origin?
\(\dfrac{13}{5}\) units
The image of \(P(1,2)\) in the \(x\)-axis (the mirror) is \(P'(1,-2)\), and the reflected ray, extended backward, passes through \(P'\). So \(N\) is where the line through \(P'(1,-2)\) and \(Q(5,3)\) meets the \(x\)-axis: \(\dfrac{y+2}{x-1}=\dfrac{5}{4}\); setting \(y=0\) gives \(x=\dfrac{13}{5}\). So \(N=\left(\dfrac{13}{5},0\right)\) and its distance from the origin is \(\dfrac{13}{5}\) units.
Similar Questions
What are the direction ratios of the line of intersection of given planes?
What is the equation of the line L?
What is the number of possible values of k for which the line joining the points (k, 1, 3) and (1, -2, k + 1) also passes through the point (15, 2, -4)?
\(ABCD\) is a square. The equations of \(AB\), \(AD\) and \(BD\) are \(y = 0\), \(x = 0\) and \(x + y - 4 = 0\) respectively. What is the equation of \(AC\)?
Important Questions from Equation of a Line
Determine the co-ordinates of the foot of the perpendicular drawn from the origin to the plane 4x - 2y + 3z - 6 = 0
The equation xy – ax – by + ab = 0 represents
What are the direction ratios of the line of intersection of given planes?
What is the equation of the line L?
- The equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and -6 is:
