Question

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

Answer 1

Answer:

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

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:

• $x_1 = -5$
• $y_1 = 1$
• $x_2 = 3$
• $y_2 = 0$

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

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

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