Question

find the distance d(p1, p2) between the points p1 and p2. p1 = (-4,5) p2 = (3,4) 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 $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-4,y_1 = 5,x_2=3,y_2 = 4$.

Step2: Calculate differences

$x_2 - x_1=3-(-4)=7$ and $y_2 - y_1=4 - 5=-1$.

Step3: Square differences and sum

$(x_2 - x_1)^2+(y_2 - y_1)^2=7^2+(-1)^2=49 + 1=50$.

Step4: Take square - root

$d=\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$.

Answer:

$5\sqrt{2}$