Question

calculate the distance between the points e = (-3, -2) and q = (2, -9) 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 $(x_1,y_1)=(-3,-2)$ and $(x_2,y_2)=(2,-9)$. Then $x_2 - x_1=2-(-3)=5$ and $y_2 - y_1=-9 - (-2)=-7$.

Step3: Calculate squares and sum

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=(-7)^2 = 49$. The sum is $25 + 49=74$.

Step4: Find distance

$d=\sqrt{74}$.

Answer:

$\sqrt{74}$