Analytical Geometry> A ray of light coming from the point (1,2...

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 , 11 Years ago

Grade 11

5 Answers

siddharth gupta

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

Last Activity: 11 Years ago

Arun Kumar

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

Last Activity: 11 Years ago

Harsh

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

Last Activity: 8 Years ago

Yash sharma

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

Last Activity: 8 Years ago

ankit singh

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Last Activity: 5 Years ago