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 \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Let \((x_1, y_1)=(17, 10)\) and \((x_2, y_2)=(- 19,5)\).

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, substitute these into the formula: \( d=\sqrt{(-36)^2+(-5)^2} \).

Step3: Calculate the squares

\((-36)^2 = 1296\) and \((-5)^2=25\). So, \( d=\sqrt{1296 + 25}=\sqrt{1321} \).

Step4: Compute the square root

\(\sqrt{1321}\approx36.345\) (rounded to the nearest thousandth).

Answer:

\( 36.345 \)