Questions: Find the distance between the points (1,3) and (0,0) Distance =

Solution Steps

To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a 2D plane, we use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

In this case, the points are \((1, 3)\) and \((0, 0)\).

We are given two points in the 2D plane:

• Point A: \((1, 3)\)
• Point B: \((0, 0)\)

To find the distance \(d\) between the points A and B, we use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates of the points:

\[ d = \sqrt{(0 - 1)^2 + (0 - 3)^2} \]

Calculating the squared differences:

\[ d = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \]

Evaluating the square root gives us:

\[ d \approx 3.1623 \]

Final Answer