Find the image of the point (2, 1) with respect to the line mirror x + y – 5 = 0.
Given: (2,1) is given point and line mirror is x + y – 5 = 0
To find:
Image of the point with respect to mirror line.
Explanation:
Let the image of A (2, 1) be B (a, b).
Let M be the midpoint of AB.
∴ Coordinates of M are
Diagram:
The point M lies on the line x + y − 5 = 0
⇒ a + b = 7 … (1)
Now, the lines x + y − 5 = 0 and AB are perpendicular.
∴ Slope of AB × Slope of CD = − 1
⇒ a – 2 = b – 1 ……(2)
Adding eq (1) and eq (2):
2a = 8
⇒ a = 4
Now, from equation (1):
4 + b = 7
⇒ b = 3
Hence, the image of the point (2, 1) with respect to the line mirror x + y − 5 = 0 is (4, 3).