Question

1. what is the length of a line segment between points (2, -2) and (-5, 6)?

a. 4 units
b. 10.6 units
c. 6.3 units
d. 12 units

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Here, \( x_1 = 2 \), \( y_1 = -2 \), \( x_2 = -5 \), \( y_2 = 6 \).

Step2: Calculate differences

Find \( x_2 - x_1 = -5 - 2 = -7 \) and \( y_2 - y_1 = 6 - (-2) = 8 \).

Step3: Square the differences

\((-7)^2 = 49\) and \( 8^2 = 64 \).

Step4: Sum the squares

\( 49 + 64 = 113 \).

Step5: Take the square root

\( d = \sqrt{113} \approx 10.6 \).

Answer:

b. 10.6 units