Q6: Find a) Draw the rectangle with vertices at \( A(-1,3), B(2,3), C(2,-3) \) and \( O(-1,-3) \). b) Write down the name of the straight line through \( A \) and \( B \). c) Write down the name of the straight line through \( A \) and \( D \).

1. **Part (a): Draw the rectangle** The rectangle has vertices \[ A(-1,3),\quad B(2,3),\quad C(2,-3),\quad O(-1,-3). \] To draw the rectangle, plot the points in the coordinate plane and connect them in order (for example, \(A \to B \to C \to O \to A\)). Notice that: - \(A\) and \(B\) have the same \(y\)-coordinate, so segment \(AB\) is horizontal. - \(B\) and \(C\) have the same \(x\)-coordinate, so segment \(BC\) is vertical. - \(C\) and \(O\) share the same \(y\)-coordinate, so segment \(CO\) is horizontal. - \(O\) and \(A\) share the same \(x\)-coordinate, so segment \(OA\) is vertical. 2. **Part (b): Name of the straight line through \(A\) and \(B\)** The points \(A(-1,3)\) and \(B(2,3)\) have the same \(y\)-coordinate. Hence, the line connecting them is horizontal with equation \[ y = 3. \] 3. **Part (c): Name of the straight line through \(A\) and \(D\)** Although the rectangle is given with vertices \(A\), \(B\), \(C\) and \(O\), the vertex \(D\) is typically taken as the fourth vertex of the rectangle. Here, assume \(D\) corresponds to the vertex \(O(-1,-3)\). The points \(A(-1,3)\) and \(O(-1,-3)\) have the same \(x\)-coordinate. Therefore, the line joining them is vertical with equation \[ x = -1. \]