Question

find the distance between the two points in simplest radical form.
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attempt 1 out of 2
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Explanation:

Step1: Identify the coordinates

Let the first point be $(-2,4)$ and the second point be $(3,9)$.

Step2: Apply the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Here $x_1=-2,y_1 = 4,x_2=3,y_2=9$. Then $d=\sqrt{(3-(-2))^2+(9 - 4)^2}$.

Step3: Simplify the expressions inside the square - root

$(3-(-2))^2=(3 + 2)^2=25$ and $(9 - 4)^2=5^2 = 25$. So $d=\sqrt{25+25}$.

Step4: Combine the terms inside the square - root

$d=\sqrt{50}$.

Step5: Simplify the radical

$\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$.

Answer:

$5\sqrt{2}$