NCERT/CBSE MATHEMATICS CLASS 11 textbook
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MISCELLANEOUS EXERCISES
Answers to NCERT/CBSE MATH (Class XI)textbook
10.STRAIGHT LINES
22. A ray of light passing through the point (1, 2) reflects on the x-axis at point A
and the reflected ray passes through the point (5, 3). Find the coordinates of A.
SOLUTION:
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NCERT/CBSE MATHEMATICS CLASS 11 textbook
http://www.TutorBreeze.com
Let the angle of incidence an reflection =x
Incident ray AB makes an angle (90 - x ) with the positive direction of the X axis,
So, its slope = m1 (say)= tan(90 - x ) = cot x
Reflected ray AC makes an angle [180- (90 - x )] with the positive direction of the X axis,
So, its slope= m 2 (say) = tan [180- (90 - x ) ] = tan(90 + x ) = - cot x
We note that m1 +m 2 = 0
Now, Letthe coordinates of A be (a,0)
The slope of line joining two points
(x1 , y1 ) and (x 2 , y 2 ) is given by
m=
( y2 − y1 )
( x2 − x1 )
The slope of AB , theline joining two points
(a,0)and (1,2 ) is given by
m1 =
( 2 − 0) = 2
(1 − a ) 1 − a
The slope of AB , theline joining two points
(a,0)and (5,3 ) is given by
m2 =
(3 − 0) = 3
(5 − a ) 5 − a
m1 +m 2 = 0
2
3
+
=0
1− a 5 − a
13
⇒a=
5
⇒
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