1. What is the distance between \( (-5,2) \) and \( (-9,2) \) ?

To find the distance between the points \((-5, 2)\) and \((-9, 2)\), we can use the distance formula. However, since both points have the same \(y\)-coordinate, we can simply calculate the distance along the \(x\)-axis. The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] In this case, we have: - \(x_1 = -5\) - \(y_1 = 2\) - \(x_2 = -9\) - \(y_2 = 2\) Since \(y_1 = y_2\), the formula simplifies to: \[ d = |x_2 - x_1| = |-9 - (-5)| = |-9 + 5| = |-4| = 4 \] Thus, the distance between the points \((-5, 2)\) and \((-9, 2)\) is \(4\).