Question

find the length of the segment with given endpoints. q(3,9) and p(7,4)

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Here, \( (x_1, y_1) = Q(3, 9) \) and \( (x_2, y_2) = P(7, 4) \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1 = 7 - 3 = 4 \) and \( y_2 - y_1 = 4 - 9 = -5 \).
Then, square these differences: \( (4)^2 = 16 \) and \( (-5)^2 = 25 \).
Add the squared differences: \( 16 + 25 = 41 \).
Take the square root: \( d = \sqrt{41} \).

Answer:

\( \sqrt{41} \) (or approximately \( 6.403 \) if a decimal approximation is needed)