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.)

Answer

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Answer

So, the distance between the points $P_1$ and $P_2$ is $\boxed{\sqrt{61}}$

Steps

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 $\boxed{\sqrt{61}}$