Question

distance and the pythagorean theorem practice
complete this assessment to review what youve learned. it will not count toward your grade.
find the distance between (2, 3) and (-4, -9). round your answer to the nearest hundredth,
if necessary. (1 point)
units

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(2,3)\) and \((x_2,y_2)=(-4,-9)\)

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

Substitute the values: \(d=\sqrt{(-4 - 2)^2+(-9 - 3)^2}\)

Step3: Calculate the differences

\(-4-2=-6\) and \(-9 - 3=-12\)
So \(d=\sqrt{(-6)^2+(-12)^2}\)

Step4: Calculate the squares

\((-6)^2 = 36\) and \((-12)^2=144\)
Then \(d=\sqrt{36 + 144}\)

Step5: Add the values inside the square - root

\(36+144 = 180\)
So \(d=\sqrt{180}\)

Step6: Simplify \(\sqrt{180}\)

\(\sqrt{180}=\sqrt{36\times5}=6\sqrt{5}\approx6\times2.236 = 13.416\approx13.42\)

Answer:

\(13.42\)