a Draw the rectangle with vertices at \( A(-1,3), B(2,3), C(2,-3) \) and \( D(-1,-3) \). b Write down the name of the straight line through \( A \) and \( B \). c Write down the coordinates of two more points on the line through \( A \) and \( B \). d Write down the name of the straight line through \( A \) and \( D \). e Write down the equation of the straight line through \( C \) and \( D \).

a) To draw the rectangle with vertices at \( A(-1,3), B(2,3), C(2,-3) \), and \( D(-1,-3) \), you would connect the points as follows: - Connect \( A(-1,3) \) to \( B(2,3) \) to form the top side of the rectangle. - Connect \( B(2,3) \) to \( C(2,-3) \) to form the right side of the rectangle. - Connect \( C(2,-3) \) to \( D(-1,-3) \) to form the bottom side of the rectangle. - Connect \( D(-1,-3) \) to \( A(-1,3) \) to form the left side of the rectangle. b) The straight line through \( A \) and \( B \) is called line \( AB \). c) Since line \( AB \) is horizontal, it has the same \( y \)-coordinate for all points on the line. The \( y \)-coordinate of \( A \) and \( B \) is 3. Therefore, two more points on line \( AB \) could be: - \( P_1(-5,3) \) - \( P_2(5,3) \) d) The straight line through \( A \) and \( D \) is called line \( AD \). e) To find the equation of the straight line through \( C \) and \( D \), we can use the two-point form of the equation of a line: \[ y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1) \] Using the coordinates of \( C(2,-3) \) and \( D(-1,-3) \): \[ y - (-3) = \frac{-3 - (-3)}{2 - (-1)}(x - 2) \] \[ y + 3 = \frac{0}{3}(x - 2) \] \[ y + 3 = 0 \] So, the equation of the straight line through \( C \) and \( D \) is \( y = -3 \).