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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)

What are the new vertices of triangle LMN, shown, if the triangle is reflected across-example-1
User MarcinR
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8.6k points

2 Answers

3 votes
D.
just count the distance between the point and the reflection line and then find the opposite of that number
User Francois Dermu
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7.1k points
1 vote

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.

User Martin Vobr
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7.4k points
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