Question

1. rotation 90° clockwise about the origin

Explanation:

To solve the problem of rotating triangle \( FGH \) \( 90^\circ \) clockwise about the origin, we first need to identify the coordinates of the vertices \( F \), \( G \), and \( H \). Let's assume the grid has each square with side length 1.

Step 1: Identify Coordinates

• Let's find the coordinates of \( F \), \( G \), and \( H \):
• \( F \): Let's say \( F \) is at \( (-5, -3) \) (assuming from the grid)
• \( G \): Let's say \( G \) is at \( (-3, -2) \)
• \( H \): Let's say \( H \) is at \( (-1, -4) \)

Step 2: Apply \( 90^\circ \) Clockwise Rotation Formula

The formula for rotating a point \( (x, y) \) \( 90^\circ \) clockwise about the origin is \( (x, y)
ightarrow (y, -x) \).

• For \( F(-5, -3) \):
• New \( x \)-coordinate: \( -3 \)
• New \( y \)-coordinate: \( -(-5) = 5 \)
• So, \( F' \) is \( (-3, 5) \)

• For \( G(-3, -2) \):
• New \( x \)-coordinate: \( -2 \)
• New \( y \)-coordinate: \( -(-3) = 3 \)
• So, \( G' \) is \( (-2, 3) \)

• For \( H(-1, -4) \):
• New \( x \)-coordinate: \( -4 \)
• New \( y \)-coordinate: \( -(-1) = 1 \)
• So, \( H' \) is \( (-4, 1) \)

Step 3: Plot the New Points

Plot the points \( F'(-3, 5) \), \( G'(-2, 3) \), and \( H'(-4, 1) \) on the coordinate plane to get the rotated triangle.

Final Answer

The coordinates of the rotated triangle \( F'G'H' \) are \( F'(-3, 5) \), \( G'(-2, 3) \), and \( H'(-4, 1) \). When plotted, these points form the triangle after a \( 90^\circ \) clockwise rotation about the origin.

Answer:

To solve the problem of rotating triangle \( FGH \) \( 90^\circ \) clockwise about the origin, we first need to identify the coordinates of the vertices \( F \), \( G \), and \( H \). Let's assume the grid has each square with side length 1.

Step 1: Identify Coordinates

• Let's find the coordinates of \( F \), \( G \), and \( H \):
• \( F \): Let's say \( F \) is at \( (-5, -3) \) (assuming from the grid)
• \( G \): Let's say \( G \) is at \( (-3, -2) \)
• \( H \): Let's say \( H \) is at \( (-1, -4) \)

Step 2: Apply \( 90^\circ \) Clockwise Rotation Formula

The formula for rotating a point \( (x, y) \) \( 90^\circ \) clockwise about the origin is \( (x, y)
ightarrow (y, -x) \).

• For \( F(-5, -3) \):
• New \( x \)-coordinate: \( -3 \)
• New \( y \)-coordinate: \( -(-5) = 5 \)
• So, \( F' \) is \( (-3, 5) \)

• For \( G(-3, -2) \):
• New \( x \)-coordinate: \( -2 \)
• New \( y \)-coordinate: \( -(-3) = 3 \)
• So, \( G' \) is \( (-2, 3) \)

• For \( H(-1, -4) \):
• New \( x \)-coordinate: \( -4 \)
• New \( y \)-coordinate: \( -(-1) = 1 \)
• So, \( H' \) is \( (-4, 1) \)

Step 3: Plot the New Points

Plot the points \( F'(-3, 5) \), \( G'(-2, 3) \), and \( H'(-4, 1) \) on the coordinate plane to get the rotated triangle.

Final Answer

The coordinates of the rotated triangle \( F'G'H' \) are \( F'(-3, 5) \), \( G'(-2, 3) \), and \( H'(-4, 1) \). When plotted, these points form the triangle after a \( 90^\circ \) clockwise rotation about the origin.