Question

What is the exact distance from (-5,1) to (3,0).​

Answer 1

Answer:

Distance =√65

Explanation:

(−5,1)=x1,y1

(3,0)=x2,y2

The distance is calculated using formula:'

Distance =√(x2−x1)2+(y2−y1)2

=√(3−(−5))2+(0−1)2

=√(3+5)2+(−1)2

=√(8)2+(−1)2

=√(64+1)

Distance =√65

Answer 2

Answer:

The distance between the two points is $\blue{\bold{\sqrt{65} \ \text{units}}}$

Step-by-step explanation:

In order to find the distance between two coordinate pairs, we can use the distance formula:

$\displaystyle \bullet \ \ \ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}∙$

Our coordinate pairs need to be labeled accordingly, so we can use this naming system:

$\bullet \ \ \ (x_1, y_1), (x_2, y_2)∙$

This assigns a name to our points:

$\bold{x_1 = -5   }$

$\bold{y_1 = 1   }$

$\bold{ x_2 = 3 }$

$\bold{y_2 = 0  }$ 

Therefore, we can plug these into the formula and solve:

$\begin{gathered}d=\sqrt{(3-(-5))^2+(0-1)^2}\\\\d=\sqrt{(8)^2+(-1)^2}\\\\d=\sqrt{8^2+1^2}\\\\d=\sqrt{64+1}\\\\d=\sqrt{65}\end{gathered}$

Therefore, the distance between the two points is $\bold{\sqrt{65} \ \text{units}}$