Question

find the distance between the two points. (4,2) (1,-3)

Explanation:

Step1: Identify the distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let $(x_1,y_1)=(1,-3)$ and $(x_2,y_2)=(4,2)$.

Step2: Calculate the difference in x - coordinates

$x_2 - x_1=4 - 1=3$.

Step3: Calculate the difference in y - coordinates

$y_2 - y_1=2-( - 3)=2 + 3 = 5$.

Step4: Square the differences and sum them

$(x_2 - x_1)^2+(y_2 - y_1)^2=3^2+5^2=9 + 25=34$.

Answer:

34