Question

What are the new vertices of triangle LMN, shown, if the triangle is reflected across the horizontal line y = 1, also shown?
    
  A. L′ = (–4,1), M′ = (3,2), N′ = (4,1)
  B. L′ = (–4,–2), M′ = (3,–4), N′ = (4,–2)
  C. L′ = (–4,0), M′ = (3,2), N′ = (4,0)
  D. L′ = (–4,0), M′ = (3,–2), N′ = (4,0)

Answer 1

D.
just count the distance between the point and the reflection line and then find the opposite of that number

Answer 2

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.