Question

question 5
what is the distance between the two bolts?
2 units
7 units
5 units
6 units
question 6
use the pythagorean theorem to find the distance between points $(-2,-3)$ and $(5,1)$.
note: your answer should be in radical form, so make sure you use the square root option!
distance =

Explanation:

Step1: Find the differences in coordinates

Let \((x_1,y_1)=(-2,-3)\) and \((x_2,y_2)=(5,1)\).
The difference in \(x -\)coordinates: \(\Delta x=x_2 - x_1=5-(-2)=7\).
The difference in \(y -\)coordinates: \(\Delta y=y_2 - y_1=1-(-3)=4\).

Step2: Apply the Pythagorean Theorem

According to the Pythagorean Theorem, the distance \(d\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(\Delta x)^2+(\Delta y)^2}\).
Substitute \(\Delta x = 7\) and \(\Delta y = 4\) into the formula: \(d=\sqrt{7^2 + 4^2}=\sqrt{49+16}\).

Step3: Calculate the result

\(d=\sqrt{65}\).

Answer:

\(\sqrt{65}\)