Answer: The correct option is (D) L′ = (–4,0), M′ = (3,–2), N′ = (4,0).
Step-by-step explanation: Given that the triangle LMN shown in the figure is reflected across the line y = 1.
We are to find the new vertices of the triangle LMN.
From the figure, we note that
the co-ordinates of the vertices of triangle LMN are L(-4, 2), M(3, 4) and N(4, 2).
We know that
if a point (x, y) is reflected across the line y = k, then its new co-ordinates are (x, 2k - y).
Therefore, after getting reflected across the line y = 1, teh new co-ordiantes of the vertices of triangle LMN will be
L(-4, 2) ⇒ L'(-4, 2 × 1 - 2) = L'(-4, 2-2) = L'(-4, 0),
M(3, 4) ⇒ M'(3, 2 × 1 - 4) = M'(3, 2-4) = M'(3, -2),
N(4, 2) ⇒ L'(4, 2 × 1 - 2) = N'(4, 2-2) = N'(4, 0).
Thus, the co-ordinates of the new vertices of triangle LMN are L'(-4, 0), M'(3, -2) ans N'(4, 0).
Option (D) is CORRECT.
