Question

find the distance between the two points. (-1,1) (4,-3)

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

Step2: Calculate differences

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

Step3: Square the differences

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=(-4)^2=16$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 16=41$.

Step5: Take the square - root

$d=\sqrt{41}$.

Answer:

$\sqrt{41}$