Assuming the straight line work as the plane mirror at a point, find the image of the point
(1,2) in the line x-2y+4=0.
16. Graphically solve the system of linear inequalities :
4x + 3y ≤ 60 , 2x − y ≥ 0 , x ≥ 3 , x ≥ 0 , y ≥ 0.
Answers
Given : point (1,2)
line x-2y+4=0.
To Find : image of the point
Solution:
image of the point be ( h , k )
Mid point of ( 1, 2) and ( h , k ) will lie on x-2y+4=0.
Mid point = ( h+ 1)/2 , ( k + 2)/2
x-2y+4=0
=> ( h + 1)/2 - 2 ( k + 2)/2 + 4 = 0
=> h + 1 - 2k - 4 + 8 = 0
=> h - 2k = - 5
Slope of line x-2y+4=0.
2y = x + 4
=> y = x/2 + 2
slope = 1/2
Slope of line joining (1 , 2) ahd h , k
= - 2
( k - 2)/(h - 1) = - 2
=> k - 2 = -2h + 2
=> 2h + k = 4
h - 2k = - 5
2h + k = 4 => 4h + 2k = 8
=> 5h = 3
=> h = 3/5
=> k = 14/5
( 3/5 , 14/5) is the image of point (1,2) in the line x-2y+4=0
(0.6 , 2.8)
Learn More:
10] IF (-2, 6) is the image of the point (4, 2) withrespect to line L = 0 ...
https://brainly.in/question/10638459
find coordinates of the point where image of an object kept at point ...
https://brainly.in/question/11463766
The image of a point (1,5) when reflected in a line LM is (9,5). Write ...
https://brainly.in/question/2659841
