What is the distance between the points (1, 2) and (4, 6)?

What is the distance between the points (1, 2) and (4, 6)?

• A. 4
• B. 5
• C. 6
• D. 7

Answer: (B)

To find the distance between two points in a two-dimensional plane, you can use the distance formula, which is derived from the Pythagorean theorem. The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] In this case, the points are (1, 2) and (4, 6). We can identify \(x_1 = 1\), \(y_1 = 2\), \(x_2 = 4\), and \(y_2 = 6\). Now, we can calculate the differences in the x and y coordinates: 1. \(x_2 - x_1 = 4 - 1 = 3\) 2. \(y_2 - y_1 = 6 - 2 = 4\) Next, we substitute these values into the distance formula: \[ d = \sqrt{(3)^2 + (4)^2} \] Calculating the squares

To find the distance between two points in a two-dimensional plane, you can use the distance formula, which is derived from the Pythagorean theorem. The distance ( d ) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by the formula:

[

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

]

In this case, the points are (1, 2) and (4, 6). We can identify (x_1 = 1), (y_1 = 2), (x_2 = 4), and (y_2 = 6).

Now, we can calculate the differences in the x and y coordinates:

1. (x_2 - x_1 = 4 - 1 = 3)

2. (y_2 - y_1 = 6 - 2 = 4)

Next, we substitute these values into the distance formula:

[

d = \sqrt{(3)^2 + (4)^2}

]

Calculating the squares