Question

calculate the distance between the points p = (-1, -4) and g = (-9, 2) in the coordinate plane. give an exact answer (not a decimal approximation).

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 $(x_1,y_1)=(-1,-4)$ and $(x_2,y_2)=(-9,2)$. Then $x_2 - x_1=-9-(-1)=-8$ and $y_2 - y_1=2 - (-4)=6$.

Step3: Calculate squares

$(x_2 - x_1)^2=(-8)^2 = 64$ and $(y_2 - y_1)^2=6^2 = 36$.

Step4: Sum and square - root

$d=\sqrt{64 + 36}=\sqrt{100}=10$.

Answer:

$10$