Question

1. find the distance between the points (1,-5) and (-3,-3). round to nearest thousandth. distance =

Explanation:

Step1: Identify 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 values

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

Step3: Calculate squares

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

Step4: Sum squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=16 + 4=20$.

Step5: Calculate distance

$d=\sqrt{20}\approx4.472$.

Answer:

$4.472$