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