Question

calculate the distance between the points h=(0, 1) and n=(5, -5) in the coordinate plane. give an exact answer (not a decimal approximation). distance:

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinate values

Let $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(5,-5)$

Step3: Substitute into formula

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

Step4: Simplify inside the square root

$d=\sqrt{5^2+(-6)^2}=\sqrt{25+36}$

Step5: Calculate final value

$d=\sqrt{61}$

Answer:

$\sqrt{61}$