Question

graph the image of the figure using the transformation given.

1. rotation \\(180^\circ\\) about the origin

1. rotation \\(180^\circ\\) about the origin

Explanation:

⚡ Using what you learned: reflections, rotations

Step 1: Identify original coordinates for Problem 1

By reading the grid for the first graph (where each grid line represents \(1\) unit and the origin is at the intersection of the axes):

• \(F = (-4, 1)\)
• \(P = (1, 3)\)
• \(K = (3, 0)\)
• \(N = (-1, -3)\)

Step 2: Apply \(180^\circ\) rotation rule for Problem 1

A rotation of \(180^\circ\) about the origin uses the coordinate rule:

$$ (x, y) ightarrow (-x, -y) $$

Applying this rule to each vertex:

• \(F' = (4, -1)\)
• \(P' = (-1, -3)\)
• \(K' = (-3, 0)\)
• \(N' = (1, 3)\)

Step 3: Identify original coordinates for Problem 2

By reading the grid for the second graph:

• \(V = (2, 0)\)
• \(J = (1, -1)\)
• \(R = (4, -3)\)
• \(Y = (5, -3)\)

Step 4: Apply \(180^\circ\) rotation rule for Problem 2

Applying the rule \((x, y)
ightarrow (-x, -y)\) to each vertex:

• \(V' = (-2, 0)\)
• \(J' = (-1, 1)\)
• \(R' = (-4, 3)\)
• \(Y' = (-5, 3)\)

Answer:

To graph the images, plot the following new coordinates on your worksheets and connect them to form the rotated shapes:

1) Rotation of \(180^\circ\) about the origin:

• \(F'\): \((4, -1)\)
• \(P'\): \((-1, -3)\)
• \(K'\): \((-3, 0)\)
• \(N'\): \((1, 3)\)

2) Rotation of \(180^\circ\) about the origin:

• \(V'\): \((-2, 0)\)
• \(J'\): \((-1, 1)\)
• \(R'\): \((-4, 3)\)
• \(Y'\): \((-5, 3)\)