Question

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

Explanation:

Step1: Identify the 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: Assign the values of the points

Let $(x_1,y_1)=(1,1)$ and $(x_2,y_2)=(3, - 4)$. Then $x_2 - x_1=3 - 1 = 2$ and $y_2 - y_1=-4 - 1=-5$.

Step3: Calculate the squares

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

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 25=29$.

Step5: Calculate the distance

$d=\sqrt{29}$.

Answer:

$\sqrt{29}$