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

Answer

Expert–verified

Hide Steps

Answer

So, the distance between the points $P_{1}$ and $P_{2}$ is $\sqrt{61}$

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 $\sqrt{61}$