Select all the pairs of points that are less than 3 units apart. \( (2.2,3.3) \) and \( (2.2,1.2) \) \( (3,-2.5) \) and \( (3,1.6) \) \( (-2.3,1) \) and \( (0.6,1) \) \( (-5.2,-3) \) and \( (-3.2,-3) \)

To determine which pairs of points are less than 3 units apart, we can use the distance formula, which is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] We will calculate the distances for each pair: 1. **Points \( (2.2,3.3) \) and \( (2.2,1.2) \):** - \( d = \sqrt{(2.2 - 2.2)^2 + (1.2 - 3.3)^2} = \sqrt{0 + (-2.1)^2} = \sqrt{4.41} \approx 2.1 \) 2. **Points \( (3,-2.5) \) and \( (3,1.6) \):** - \( d = \sqrt{(3 - 3)^2 + (1.6 - (-2.5))^2} = \sqrt{0 + (4.1)^2} = \sqrt{16.81} \approx 4.1 \) 3. **Points \( (-2.3,1) \) and \( (0.6,1) \):** - \( d = \sqrt{(0.6 - (-2.3))^2 + (1 - 1)^2} = \sqrt{(2.9)^2 + 0} = \sqrt{8.41} \approx 2.9 \) 4. **Points \( (-5.2,-3) \) and \( (-3.2,-3) \):** - \( d = \sqrt{(-3.2 - (-5.2))^2 + (-3 - (-3))^2} = \sqrt{(2.0)^2 + 0} = \sqrt{4} = 2 \) Now, we determine which distances are less than 3 units: - \( (2.2,3.3) \) and \( (2.2,1.2) \) are **2.1 units apart** (less than 3). - \( (3,-2.5) \) and \( (3,1.6) \) are **4.1 units apart** (not less than 3). - \( (-2.3,1) \) and \( (0.6,1) \) are **2.9 units apart** (less than 3). - \( (-5.2,-3) \) and \( (-3.2,-3) \) are **2 units apart** (less than 3). Thus, the pairs of points that are less than 3 units apart are: - \( (2.2,3.3) \) and \( (2.2,1.2) \) - \( (-2.3,1) \) and \( (0.6,1) \) - \( (-5.2,-3) \) and \( (-3.2,-3) \)