Question

you want to find the distance between $(-3, -12)$ and $(7, -16)$. which of the following equations will help you find the distance between the points?
\\(\circ\\) $d = \sqrt{(-3 - (-16)) + (-12 - 7)}$
\\(\circ\\) $d = \sqrt{(-3 - 7)^2 - (-16 - (-12))^2}$
\\(\circ\\) $d = \sqrt{(-3 - (-12))^2 + (7 - (-16))^2}$
\\(\circ\\) $d = \sqrt{(-3 - 7)^2 + (-12 - (-16))^2}$

Explanation:

Step1: Recall the distance formula

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

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

For the points \((-3, -12)\) and \((7, -16)\), we have \(x_1=-3\), \(y_1 = - 12\), \(x_2 = 7\), \(y_2=-16\).

Step3: Substitute into the formula

Substitute these values into the distance formula:
\(x_1 - x_2=-3 - 7\) and \(y_1 - y_2=-12-(-16)\).
So the distance formula becomes \( d=\sqrt{(-3 - 7)^2+(-12 - (-16))^2} \), which matches the last option.

Answer:

\( d = \sqrt{(-3 - 7)^2 + (-12 - (-16))^2} \) (the last option)