Grade 11Analytical Geometry

A ray of light coming from the point (1,2) is reflected at a point A on the x-axis and then passes through the point (5,3). What are the co-ordinates of point A?

Rituraj Singh

12 Years agoGrade 11

5 Answers

siddharth gupta

12 Years ago

Assume the x-axis to be a mirror.

take the image of (1,2) in x-axis i.e(1,-2).

as we know that reflected ray when extended back passes through the image of a point on incident ray i.e reflected ray passes through (1,-2) and (5,3).

.^..from two point form eqn of refl.ray=5x-4y-13=0.

put y=0 .^..point of incidence=(13/5,0).

with regards

SIDDHARTH GUPTA

Arun Kumar

12 Years ago

Hello

$\\ tan(\theta)={2 \over 1-x} \\tan(\pi -\theta)={3 \over 5-x}=-tan(\theta)=-{2 \over 1-x} \\3x-3=5-x \\=>4x=8 \\=>x=2$

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

Harsh

8 Years ago

Assume the x-axis to be a mirror.

take the image of (1,2) in x-axis i.e(1,-2).

as we know that reflected ray when extended back passes through the image of a point on incident ray i.e reflected ray passes through (1,-2) and (5,3).

.^..from two point form eqn of refl.ray=5x-4y-13=0.

put y=0 .^..point of incidence=(13/5,0).

with regards

Harsh panwar

IIT ROORKEE

AIR 55

Yash sharma

8 Years ago

Assume the x-axis to be a mirror.take the image of (1,2) in x-axis i.e(1,-2).as we know that reflected ray when extended back passes through the image of a point on incident ray i.e reflected ray passes through (1,-2) and (5,3)....from two point form eqn of refl.ray=5x-4y-13=0.put y=0 ...point of incidence=(13/5,0) Aman bansal AIR1

ankit singh

5 Years ago

A ray of light passing through the point P(1,2) reflects on the x-axis at the point A and the reflected ray passes ... ∴m1=-m2. Let coordinates of point A is (a,0). Then, 2-01-a=-3-05-a ... A ray of light coming fromthe point (1, 2) is reflected at a.