Question

the distance formula
find the distance between each pair of points.

1. (7, 3), (-1, -4)

) = \sqrt{(7 - -1)^2 + (3 - -4)^2}

Explanation:

Step1: Recall Distance Formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} \). For points \((7, 3)\) and \((-1, -4)\), \( x_1 = 7, y_1 = 3, x_2 = -1, y_2 = -4 \).

Step2: Substitute Values

Substitute into the formula: \( d = \sqrt{(7 - (-1))^2 + (3 - (-4))^2} = \sqrt{(8)^2 + (7)^2} \).

Step3: Calculate Squares

\( 8^2 = 64 \), \( 7^2 = 49 \). So, \( d = \sqrt{64 + 49} \).

Step4: Sum and Simplify

\( 64 + 49 = 113 \), so \( d = \sqrt{113} \approx 10.63 \).

Answer:

The distance between \((7, 3)\) and \((-1, -4)\) is \(\sqrt{113}\) (or approximately \(10.63\)).