Question

find the distance between the pair of points.
(17,10) and (-19,5)

the distance is
(round to the nearest thousandth as needed.)

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, \( x_1 = 17\), \( y_1 = 10\), \( x_2=- 19\), \( y_2 = 5\).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1=-19 - 17=-36\) and \( y_2 - y_1=5 - 10=-5\).
Then, find the squares: \((x_2 - x_1)^2=(-36)^2 = 1296\) and \((y_2 - y_1)^2=(-5)^2 = 25\).

Step3: Sum the squares and take the square root

Sum the squares: \(1296 + 25=1321\).
Take the square root: \(d=\sqrt{1321}\approx36.345\) (rounded to the nearest thousandth).

Answer:

\(36.345\)