Which of these points are 5 units away from \( (-6,-3) \) ? Select all that appl \begin{tabular}{lll|l|}\( (-2,0) \) & \( (-3,-7) \) & \( (-2,-7) \)\end{tabular}

To determine which points are 5 units away from \( (-6,-3) \), we can use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Setting \( d = 5 \) gives us the equation: \[ \sqrt{(x + 6)^2 + (y + 3)^2} = 5 \] Now, let's plug in each point: 1. For \( (-2,0) \): \[ d = \sqrt{((-2) + 6)^2 + (0 + 3)^2} = \sqrt{(4)^2 + (3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \quad \text{(This point works.)} \] 2. For \( (-3,-7) \): \[ d = \sqrt{((-3) + 6)^2 + ((-7) + 3)^2} = \sqrt{(3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \quad \text{(This point works.)} \] 3. For \( (-2,-7) \): \[ d = \sqrt{((-2) + 6)^2 + ((-7) + 3)^2} = \sqrt{(4)^2 + (-4)^2} = \sqrt{16 + 16} = \sqrt{32} \neq 5 \quad \text{(This point does NOT work.)} \] Thus, the points that are 5 units away from \( (-6,-3) \) are \( (-2,0) \) and \( (-3,-7) \).