Question 4, 2 Find the distance $d\left(P_{1}, P_{2}\right)$ between the points $P_{1}$ and $P_{2}$. \[ P_{1}=(-2,5) ; P_{2}=(4,0) \] $d\left(P_{1}, P_{2}\right)=\square$ (Type an exact answer, using radicals as needed.)

Step 1 ：\(d(P_1, P_2) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Step 2 ：Substitute \(P_1 = (-2, 5)\) and \(P_2 = (4, 0)\) into the formula

Step 3 ：\(d(P_1, P_2) = \sqrt{(4 - (-2))^2 + (0 - 5)^2}\)

Step 4 ：Solve inside the parentheses: \(d(P_1, P_2) = \sqrt{(6)^2 + (-5)^2}\)

Step 5 ：Square the numbers inside the square root: \(d(P_1, P_2) = \sqrt{36 + 25}\)

Step 6 ：Add the numbers inside the square root: \(d(P_1, P_2) = \sqrt{61}\)

Step 7 ：So, the distance between the points \(P_1\) and \(P_2\) is \(\boxed{\sqrt{61}}\)