Question

determine the distance between the points (-5, -3) and (-10, -8).
○ √7 units
○ √48 units
○ √50 units
○ √250 units

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-5,-3)\) and \((x_2,y_2)=(-10,-8)\)

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

Substitute the values: \(d=\sqrt{(-10-(-5))^2+(-8 - (-3))^2}\)

Step3: Simplify the expressions inside the square root

\(-10-(-5)=-10 + 5=-5\) and \(-8-(-3)=-8 + 3=-5\)
So \(d=\sqrt{(-5)^2+(-5)^2}\)

Step4: Calculate the squares

\((-5)^2 = 25\), then \(d=\sqrt{25+25}=\sqrt{50}\)

Answer:

\(\sqrt{50}\) units