Question

Silvia is trying to calculate the distance between point A(2, 6) and point B(5, 1). Which mathematical expression or formula will she use?

Answer 1

The distance between two points A(2, 6) and B(5, 1) is calculated using the distance formula derived from the Pythagorean theorem, which is D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. For these points, the distance is \sqrt{34} units.

Step-by-step explanation:

Silvia is trying to calculate the distance between point A(2, 6) and point B(5, 1). To find the distance between two points on a coordinate plane, we use the distance formula which is derived from the Pythagorean theorem. The distance formula is:

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

For points A(2, 6) and B(5, 1), we plug in the coordinates into the formula as follows:

D = \sqrt{(5 - 2)^2 + (1 - 6)^2}

D = \sqrt{3^2 + (-5)^2}

D = \sqrt{9 + 25}

D = \sqrt{34}

Therefore, the distance between point A and B is \sqrt{34} units.