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