Question

calculate the distance between the points ( a=(-3,-4) ) and ( c=(2,3) ) to the second - place alone. give an exact answer (no a decimal approximation).

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-3,y_1 = - 4,x_2=2,y_2 = 3$.

Step2: Calculate differences

$x_2 - x_1=2-(-3)=5$ and $y_2 - y_1=3 - (-4)=7$.

Step3: Square the differences

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=7^2 = 49$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 49=74$.

Step5: Take square - root

$d=\sqrt{74}$

Answer:

$\sqrt{74}$