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 determine the coordinates of the vertices \( F \), \( G \), and \( H \). Let's assume the coordinates from the grid:

• Let’s find the coordinates:
• Let’s assume \( F = (-5, -3) \), \( G = (-3, -2) \), \( H = (-1, -4) \) (we need to confirm the grid positions, but generally, for a \( 90^\circ \) clockwise rotation about the origin, the transformation rule is \( (x, y) \to (y, -x) \)).

Step 1: Recall the rotation rule

The rule for a \( 90^\circ \) clockwise rotation about the origin is:
If a point \( (x, y) \) is rotated \( 90^\circ \) clockwise about the origin, the new coordinates \( (x', y') \) are given by:
\[
(x, y) \to (y, -x)
\]

Step 2: Apply the rule to each vertex

For point \( F(-5, -3) \):

Using the rule \( (x, y) \to (y, -x) \):
\( x = -5 \), \( y = -3 \)
New \( x' = y = -3 \)
New \( y' = -x = -(-5) = 5 \)
So, \( F' = (-3, 5) \)

For point \( G(-3, -2) \):

\( x = -3 \), \( y = -2 \)
New \( x' = y = -2 \)
New \( y' = -x = -(-3) = 3 \)
So, \( G' = (-2, 3) \)

For point \( H(-1, -4) \):

\( x = -1 \), \( y = -4 \)
New \( x' = y = -4 \)
New \( y' = -x = -(-1) = 1 \)
So, \( H' = (-4, 1) \)

Step 3: Plot the new points

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

Final Answer

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

Answer:

To solve the problem of rotating triangle \( FGH \) \( 90^\circ \) clockwise about the origin, we first need to determine the coordinates of the vertices \( F \), \( G \), and \( H \). Let's assume the coordinates from the grid:

• Let’s find the coordinates:
• Let’s assume \( F = (-5, -3) \), \( G = (-3, -2) \), \( H = (-1, -4) \) (we need to confirm the grid positions, but generally, for a \( 90^\circ \) clockwise rotation about the origin, the transformation rule is \( (x, y) \to (y, -x) \)).

Step 1: Recall the rotation rule

The rule for a \( 90^\circ \) clockwise rotation about the origin is:
If a point \( (x, y) \) is rotated \( 90^\circ \) clockwise about the origin, the new coordinates \( (x', y') \) are given by:
\[
(x, y) \to (y, -x)
\]

Step 2: Apply the rule to each vertex

For point \( F(-5, -3) \):

Using the rule \( (x, y) \to (y, -x) \):
\( x = -5 \), \( y = -3 \)
New \( x' = y = -3 \)
New \( y' = -x = -(-5) = 5 \)
So, \( F' = (-3, 5) \)

For point \( G(-3, -2) \):

\( x = -3 \), \( y = -2 \)
New \( x' = y = -2 \)
New \( y' = -x = -(-3) = 3 \)
So, \( G' = (-2, 3) \)

For point \( H(-1, -4) \):

\( x = -1 \), \( y = -4 \)
New \( x' = y = -4 \)
New \( y' = -x = -(-1) = 1 \)
So, \( H' = (-4, 1) \)

Step 3: Plot the new points

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

Final Answer

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