Question

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

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-3,-4)\) and \((x_2,y_2)=(3,-3)\).

Step2: Apply the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values: \(d=\sqrt{(3-(-3))^2+(-3 - (-4))^2}\).

Step3: Simplify the expressions inside the square - root

First, \(3-(-3)=3 + 3=6\) and \(-3-(-4)=-3 + 4 = 1\).
So, \(d=\sqrt{6^2+1^2}\).

Step4: Calculate the squares

\(6^2 = 36\) and \(1^2=1\). Then \(d=\sqrt{36 + 1}\).

Step5: Add the numbers inside the square - root

\(36+1 = 37\). So, \(d=\sqrt{37}\).

Answer:

\(\sqrt{37}\approx6.08\) (rounded to two decimal places)