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)

 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.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

the answer is 24

step-by-step explanation: