Question

kuta software - infinite algebra 1
the distance formula
find the distance between each pair of points

1. (7, 3), (-1, -4)
2. (6, -7), (3, -5)
3. (5, -8), (-8, 6)

Explanation:

Step1: Recall Distance Formula

The distance \( d \) 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: Apply Formula to \((7, 3)\) and \((-1, -4)\)

Substitute \( x_1 = 7, y_1 = 3, x_2 = -1, y_2 = -4 \):
\( d = \sqrt{(-1 - 7)^2 + (-4 - 3)^2} = \sqrt{(-8)^2 + (-7)^2} \)
Simplify squares: \( \sqrt{64 + 49} = \sqrt{113} \) (Note: Original work had an error, \( 64 + 49 = 113 \), but distance is \( \sqrt{113} \), not \( 113 \).)

Step3: Apply Formula to \((6, -7)\) and \((3, -5)\)

Substitute \( x_1 = 6, y_1 = -7, x_2 = 3, y_2 = -5 \):
\( d = \sqrt{(3 - 6)^2 + (-5 - (-7))^2} = \sqrt{(-3)^2 + (2)^2} = \sqrt{9 + 4} = \sqrt{13} \) (Correcting the handwritten error in the problem.)

Step4: Apply Formula to \((5, -8)\) and \((-8, 6)\)

Substitute \( x_1 = 5, y_1 = -8, x_2 = -8, y_2 = 6 \):
\( d = \sqrt{(-8 - 5)^2 + (6 - (-8))^2} = \sqrt{(-13)^2 + (14)^2} \)
Simplify squares: \( \sqrt{169 + 196} = \sqrt{365} \)

Answer:

1. \( \sqrt{113} \) (Correcting the original mistake), 3) \( \sqrt{13} \), 5) \( \sqrt{365} \)