1) A square has vertices \(A = (-4, 0), B = (-4, 4), C = (0, 4),\) and \(O = (0, 0)\). When the square is rotated \(90^{\circ}\) clockwise about the origin, points \(A, B,\) and \(C\) are rotated to points \(E, F,\) and \(G\) respectively. Find the area of the polygon with vertices at \(A, B, F,\) and \(G\).
2) \(Q(-2, 2)\) is rotated \(90^{\circ}\) counterclockwise about the point \((3, 1)\). Find \(Q’\).
3) Rotate \(y = 3x – 8\); \( 90^{\circ}\) clockwise
a) about the \(x\)-intercept. Write the equation of the image.
b) about the \(y\)-intercept. Write the equation of the image.
4) Rotate \(y = -\Large\frac{1}{4}\normalsize x + 3\); \( 180^{\circ}\)
a) about the \(x\)-intercept. Write the equation of the image.
b) about the \(y\)-intercept. Write the equation of the image.
5) Rotate the line the given number of degrees (i) about the \(x\)-intercept and (ii) about the \(y\)-intercept. Write the equation of each image.
a) \(y = 2x – 3\); \( 90^{\circ}\) counterclockwise
b) \( y = \Large\frac{1}{2}\normalsize x + 5\); \(270^{\circ}\) counterclockwise
6) The line \(y = -2x + 5\) is rotated about the origin by \(90^{\circ}\) counterclockwise. Find where the image of the line crosses the line \(y = x\).
2) \(Q(-2, 2)\) is rotated \(90^{\circ}\) counterclockwise about the point \((3, 1)\). Find \(Q’\).
3) Rotate \(y = 3x – 8\); \( 90^{\circ}\) clockwise
a) about the \(x\)-intercept. Write the equation of the image.
b) about the \(y\)-intercept. Write the equation of the image.
4) Rotate \(y = -\Large\frac{1}{4}\normalsize x + 3\); \( 180^{\circ}\)
a) about the \(x\)-intercept. Write the equation of the image.
b) about the \(y\)-intercept. Write the equation of the image.
5) Rotate the line the given number of degrees (i) about the \(x\)-intercept and (ii) about the \(y\)-intercept. Write the equation of each image.
a) \(y = 2x – 3\); \( 90^{\circ}\) counterclockwise
b) \( y = \Large\frac{1}{2}\normalsize x + 5\); \(270^{\circ}\) counterclockwise
6) The line \(y = -2x + 5\) is rotated about the origin by \(90^{\circ}\) counterclockwise. Find where the image of the line crosses the line \(y = x\).
7) Rotate \(\triangle WHY\) about \(C\) by
a) \(90^{\circ}\) clockwise
b) \(180^{\circ}\)
a) \(90^{\circ}\) clockwise
b) \(180^{\circ}\)
8) Rotate \(\triangle NOT\) about \(D\) by
a) \(270^{\circ}\) clockwise
b) \(180^{\circ}\)
a) \(270^{\circ}\) clockwise
b) \(180^{\circ}\)