Question

calculate the distance between the points f = (-6, 9) and e = (-3, 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 $(x_1,y_1)=(-6,9)$ and $(x_2,y_2)=(-3,2)$. Then $x_2 - x_1=-3-(-6)=3$ and $y_2 - y_1=2 - 9=-7$.

Step3: Calculate squared - differences

$(x_2 - x_1)^2=3^2 = 9$ and $(y_2 - y_1)^2=(-7)^2 = 49$.

Step4: Sum squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=9 + 49=58$.

Step5: Find distance

$d=\sqrt{58}$.

Answer:

$\sqrt{58}$