Question

you want to find the distance between (-10, -21) and (3, 32). which of the following equations will help you find the distance between the points?

○ $d = \sqrt{(3 - (-10))^2 - (32 - (-10))^2}$

○ $d = \sqrt{(3 - (-10)) + (32 - (-10))}$

○ $d = \sqrt{(-10 - (-21))^2 + (3 - 32)^2}$

○ $d = \sqrt{(3 - (-10))^2 + (32 - (-21))^2}$

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 \(x_1, y_1, x_2, y_2\)

For the points \((-10, -21)\) and \((3, 32)\), we have \(x_1=-10\), \(y_1 = - 21\), \(x_2 = 3\), \(y_2=32\).

Step3: Substitute into the formula

Substitute these values into the distance formula:
\(x_2 - x_1=3-(-10)\) and \(y_2 - y_1 = 32-(-21)\)
So the distance \(d=\sqrt{(3 - (-10))^2+(32 - (-21))^2}\)

Answer:

\( d = \sqrt{(3 - (-10))^2 + (32 - (-21))^2} \) (the fourth option)