Questions: Graph the polygon with the given vertices and its image after a reflection in the given line J(3,-5), K(4,-1), L(0,-3); y=-3

Solution Steps

The vertices of the polygon are given as:

• \( J(3, -5) \)
• \( K(4, -1) \)
• \( L(0, -3) \)

The line of reflection is \( y = -3 \).

To reflect a point across a horizontal line \( y = c \), the y-coordinate of the point is transformed as follows:

• If the original point is \((x, y)\), the reflected point will be \((x, 2c - y)\).

For each vertex:

• For \( J(3, -5) \):

  • Reflected y-coordinate: \( 2(-3) - (-5) = -6 + 5 = -1 \)
  • Reflected point: \( J'(3, -1) \)

• For \( K(4, -1) \):

  • Reflected y-coordinate: \( 2(-3) - (-1) = -6 + 1 = -5 \)
  • Reflected point: \( K'(4, -5) \)

• For \( L(0, -3) \):

  • Reflected y-coordinate: \( 2(-3) - (-3) = -6 + 3 = -3 \)
  • Reflected point: \( L'(0, -3) \)

The reflected vertices are:

• \( J'(3, -1) \)
• \( K'(4, -5) \)
• \( L'(0, -3) \)

Plot these points on the graph and connect them to form the reflected polygon.

Final Answer