Question

calculate the distance between the points l=(1, -1) and p=(6, -9) in the coordinate plane. round your answer to the nearest hundredth.

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 $(x_1,y_1)=(1, - 1)$ and $(x_2,y_2)=(6,-9)$. Then $x_2 - x_1=6 - 1 = 5$ and $y_2 - y_1=-9-( - 1)=-9 + 1=-8$.

Step3: Calculate squares

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=(-8)^2 = 64$.

Step4: Sum squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 64=89$.

Step5: Calculate distance

$d=\sqrt{89}\approx9.43$.

Answer:

$9.43$