Question

find the distance between the two points. enter the number that goes beneath the radical symbol. (1,4) (-2,-3)

Explanation:

Step1: Identify distance - formula values

Let $(x_1,y_1)=(-2,-3)$ and $(x_2,y_2)=(1,4)$.

Step2: Calculate the difference in x - coordinates

$\Delta x=x_2 - x_1=1-(-2)=3$

Step3: Calculate the difference in y - coordinates

$\Delta y=y_2 - y_1=4-(-3)=7$

Step4: Apply the distance formula

The distance $d$ 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, we want the value inside the square - root, which is $(x_2 - x_1)^2+(y_2 - y_1)^2$. Substitute $\Delta x = 3$ and $\Delta y = 7$ into it: $(x_2 - x_1)^2+(y_2 - y_1)^2=3^2+7^2=9 + 49=58$.

Answer:

58