Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places.
(0,0) and (-3,4)
the distance between the points is units.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(-3,4)\).

Step2: Substitute the values into the formula

Substitute \(x_1 = 0,y_1 = 0,x_2=-3,y_2 = 4\) into the formula:

$$
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$$

Step3: Calculate the squares

Calculate \((-3)^2=9\) and \(4^2 = 16\). Then \(d=\sqrt{9 + 16}\).

Step4: Add the values inside the square - root

\(9+16 = 25\), so \(d=\sqrt{25}\).

Step5: Simplify the square - root

Since \(\sqrt{25}=5\).

Answer:

\(5\)