Question

find the distance between the points (-10, -9) and (-5, 3).
round decimals to the nearest tenth.
units

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-10,-9)\) and \((x_2,y_2)=(-5,3)\)

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

Substitute the values: \(d=\sqrt{(-5-(-10))^2+(3 - (-9))^2}\)

Step3: Simplify the expressions inside the square - root

\(-5-(-10)=-5 + 10=5\) and \(3-(-9)=3 + 9 = 12\)
So \(d=\sqrt{5^2+12^2}\)

Step4: Calculate the squares

\(5^2 = 25\) and \(12^2=144\)
Then \(d=\sqrt{25 + 144}=\sqrt{169}\)

Step5: Find the square - root

\(\sqrt{169}=13\)

Answer:

\(13\)