What is the distance between the points (a,b) and (-a,-b)

Correct option is B

Given:

The coordinates of the two points are (a, b) and (-a, -b).

Formula Used:

The distance between two points $$(x_1, y_1)$$​ and $$(x_2, y_2)$$​ is calculated using the distance formula:

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

Solution:

1. Substituting the coordinates (a, b) and (-a, -b) into the distance formula:

​$$d = \sqrt{((-a) - a)^2 + ((-b) - b)^2}$$​​

2. Simplifying the expression:

​$$d = \sqrt{(-2a)^2 + (-2b)^2} = \sqrt{4a^2 + 4b^2}$$​​

3. Taking the square root:

​$$d = 2\sqrt{a^2 + b^2}$$​​

Thus, the distance between the points is $$2\sqrt{a^2 + b^2}$$​, which corresponds to option B.