find the coordinates of the vertices of the triangle after a reflection across the line x= -1 and then across the x-axis

 C

Step-by-step explanation:

Reflection across x = -1

The simplest way to calculate the new coordinates is to draw x = -1, count how many units away the point is from x = -1, then count the same number of units from x = -1 in the OPPOSITE direction to find the reflection. (see attachment)

J = (0, 0) is 1 unit to the right of x = -1

J' = (-2, 0) is 1 unit to the left of x = -1

K = (1, 4) is 2 units to the right of x = -1

K' = (-3, 4) is 2 units to the left of x = -1

L = (3, 3) is 4 units to the right of x = -1

L' = (-5, 3) is 4 units to the left of x = -1

Reflection across x-axis

Change the sign of the y-value:  (x, y) → (x, -y)

J' = (-2, 0)           J'' = (-2, 0)

K' = (-3, 4)           K'' = (-3, -4)  

L' = (-5, 3)            L' = (-5, -3)