Questions: Find the distance between the points (5,8) and (10,1). Write your answer as a whole number or a fully simplified radical expression. Do not round. units

Solution Steps

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the distance formula: \[ \text{distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] We will substitute the given points \((5, 8)\) and \((10, 1)\) into this formula and calculate the distance.

We are given the points \( (5, 8) \) and \( (10, 1) \).

Using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] we substitute \( x_1 = 5 \), \( y_1 = 8 \), \( x_2 = 10 \), and \( y_2 = 1 \): \[ d = \sqrt{(10 - 5)^2 + (1 - 8)^2} \]

Calculating the differences: \[ d = \sqrt{(5)^2 + (-7)^2} = \sqrt{25 + 49} = \sqrt{74} \]

The numerical value of \( \sqrt{74} \) is approximately \( 8.6023 \) when rounded to four significant digits.

Final Answer