Question

what is the distance between the points (12, 42) and (19, 37)?
○ √72 units
○ 5√3 units
○ 6√2 units
○ √74 units

Explanation:

Step1: Recall the distance formula

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

Step2: Identify the coordinates

Here, \( x_1 = 12 \), \( y_1 = 42 \), \( x_2 = 19 \), and \( y_2 = 37 \).

Step3: Substitute into the formula

First, calculate the differences: \( x_2 - x_1 = 19 - 12 = 7 \) and \( y_2 - y_1 = 37 - 42 = -5 \).
Then, square these differences: \( (7)^2 = 49 \) and \( (-5)^2 = 25 \).
Add the squared differences: \( 49 + 25 = 74 \).
Finally, take the square root: \( d = \sqrt{74} \).

Answer:

$\sqrt{74}$ units (corresponding to the option "√74 units")