Question

find the distance d(p1,p2) between the points p1 and p2. p1=(a,1) p2=(0,0) d(p1,p2)=□ (simplify your answer. type an exact answer, using radicals as needed)

Explanation:

Step1: Recall distance formula

The distance formula between two points $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here $x_1=a,y_1 = 1,x_2=0,y_2 = 0$.

Step2: Substitute values

Substitute the values into the formula: $d=\sqrt{(0 - a)^2+(0 - 1)^2}=\sqrt{(-a)^2+(- 1)^2}$.

Step3: Simplify

Since $(-a)^2=a^2$ and $(-1)^2 = 1$, we get $d=\sqrt{a^{2}+1}$.

Answer:

$\sqrt{a^{2}+1}$