Question

Find the image of the following points as directed.
(i) Point A(4, 5) reflected in the line x = 6.
(ii) Point B(-3, 2) reflected in the line x = -5.
(ii) Point C(3, 6) reflected in the line y = -2.
(iv) Point D(-2,-5) reflected in the line y = 5.​

Answer 1

Given : points and reflected through line

To Find : image of the following points as directed.

(i) Point A(4, 5) reflected in the line x = 6.

(ii) Point B(-3, 2) reflected in the line x = -5.

(ii) Point C(3, 6) reflected in the line y = -2.

(iv) Point D(-2,-5) reflected in the line y = 5.​

Solution:

(i) Point A(4, 5) reflected in the line x = 6

Image will be ( 8 , 5)     ( as reflected through x = 6 , a line parallel to y axis hence no change in y coordinates )

and x = 6 will be mid point of  x coordinate of  4 and image of 4

Hence ( 4 + 8 )/2 = 6

(ii) Point B(-3, 2) reflected in the line x = -5.

Image = ( -7 , 2)      ( similarly as above case )

(ii) Point C(3, 6) reflected in the line y = -2.

Image will be ( 3 , -10)     ( as reflected through y = -2 , a line parallel to x axis hence no change in y coordinates )

and y = -2 will be mid point of  y coordinate of  6 and image of 6

Hence ( 6 + (-10) )/2 = -2

(iv) Point D(-2,-5) reflected in the line y = 5.

Image will be ( -2 ,15)     ( similarly as above case )

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