Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the line to be a plane mirror.

image of a point in a straight line 

ncert cbse chapter 10 straight lines miscellaneous exercise

 

 Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the
line to be a plane mirror. 

or find the foot of the perpendicular of (3, 8) in the line x +3y = 7

let P=(3,8) 

let M be its foot of the perpendicular on the given line x +3y = 7

PM perpendicular to  x +3y = 7 means

equation of PM is of the form 3x - y +k =0 ----------(1)

[ because bx-ay+k = 0 is perpendicular to ax+by+c=0 ]

{3x - y +k =0 } passes through P(3,8)

means 3(3)-8+k = 0 so that k =(-1) so that 

equation of PM is 3x-y-1=0 using equation(1).

now solving the two equations 

[ x + 3y = 7 ] x3

3x - y = 1

solving

3x + 9y = 21

3x -   y     = 1

subtracting

10y = 20

y = 2

x +3(2)=7

x =1

so that M=(1,2) which is the foot of the perpendicular.

let Q(h,k) be the image of P(3,8) in the given line

Mid point of PQ is [{(h+3)/2} , {(k+8)/2}]

but the midpoint is M(1,2)

therfore

{(h+3)/2} = 1  and {(k+8)/2} = 2

h+3 =2        and k+8 =4

h=(-1)  and k =(-4)

image is ( -1 , -4 )

ncert cbse chapter 10 straight lines miscellaneous exercise

24.  A person standing at the junction (crossing) of two straight paths represented by the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he should follow.

solution

 

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 

 21. Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 =0

solution

 

Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the
line to be a plane mirror.

solution 

ncert cbse chapter 9 sequences and series miscellaneous exercise

 

 32.

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on the second day. 4 more workers dropped out on the third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was finished

solution

 

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