Question

what is the distance between the two points shown below? 200√10 units 200 units 50√2 units 500 units

Explanation:

Step1: Recall distance formula

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

Step2: Assume points

Let's assume the two - point coordinates are found from the grid. Suppose the first point is $(x_1,y_1)$ and the second is $(x_2,y_2)$. If we assume the grid has a scale where each square represents a certain unit (say 100 units for simplicity). After identifying the coordinates of the two points from the grid, if the difference in $x$ - coordinates $\Delta x=x_2 - x_1 = 600$ and the difference in $y$ - coordinates $\Delta y=y_2 - y_1 = 200$.

Step3: Calculate distance

Substitute into the formula: $d=\sqrt{(600)^2+(200)^2}=\sqrt{360000 + 40000}=\sqrt{400000}=200\sqrt{10}$ units.

Answer:

$200\sqrt{10}$ units