Question

directions
answer the question below to check your understanding and move forward in the course! this quiz is not graded.
which of the following distance formulas would be correct given the points (-4,-6) and (9,8)?
select the correct answer
√(9 - (-4))² + (8 - (-5))²
√(-4 + 9)² + (-6 + 8)²
√(9 - 4)² + (8 - 6)²
√(-4 - 9)² + (-6 - 8)²

Explanation:

Step1: Recall the distance formula

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

Step2: Identify \(x_1,y_1,x_2,y_2\)

Given the points \((-4,-6)\) and \((9,8)\), we have \(x_1=-4,y_1 = -6,x_2=9,y_2=8\).

Step3: Substitute into the formula

Substitute into \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), we get \(d=\sqrt{(9-(-4))^2+(8 - (-6))^2}=\sqrt{(9 + 4)^2+(8+6)^2}\). Also, using \(d=\sqrt{(x_1 - x_2)^2+(y_1 - y_2)^2}\), we have \(d=\sqrt{(-4 - 9)^2+(-6 - 8)^2}\).

Answer:

\(\sqrt{(-4 - 9)^2+(-6 - 8)^2}\)