Question

find the distance between the points (8, 7) and (9, 0). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Recall the distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Step2: Identify the coordinates

Here, \( x_1 = 8 \), \( y_1 = 7 \), \( x_2 = 9 \), and \( y_2 = 0 \).

Step3: Substitute into the formula

Substitute the values into the distance formula:
\[

$$\begin{align*} d&=\sqrt{(9 - 8)^2 + (0 - 7)^2}\\ &=\sqrt{(1)^2 + (-7)^2}\\ &=\sqrt{1 + 49}\\ &=\sqrt{50} \end{align*}$$

\]

Step4: Simplify the radical

Simplify \( \sqrt{50} \). We know that \( 50 = 25\times2 \), so \( \sqrt{50}=\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}=5\sqrt{2} \).

Answer:

\( 5\sqrt{2} \)