Question

1. (6, -7), (3, -5)\

) = \sqrt{(6 - \quad)^2 + (-7 - \quad)^2}

Explanation:

Step1: Recall 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 Coordinates

For points \((6, -7)\) and \((3, -5)\), we have \(x_1 = 6\), \(y_1=-7\), \(x_2 = 3\), \(y_2=-5\).
Substitute into the formula: \(d=\sqrt{(6 - 3)^2+(-7-(-5))^2}\). So the blanks should be filled with \(3\) (for the \(x\)-coordinate difference) and \(- 5\) (for the \(y\)-coordinate difference, since \(-7-(-5)=-7 + 5=-2\), and we use \(y_2=-5\) in the formula \((y_1 - y_2)\)).

Answer:

The first blank (inside the first parenthesis) is \(3\) and the second blank (inside the second parenthesis) is \(-5\), so the filled formula is \(d=\sqrt{(6 - 3)^2+(-7-(-5))^2}\)