Question

What is the distance between the points A(2, -1) and B(-4, 2)

Answer 1

The distance between two points A(2, -1) and B(-4, 2) is $3 \sqrt{5}$ units

Solution:

Given that two points are A(2, -1) and B(-4, 2)

To find: distance between two points

The distance between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ is given as:

$Distance(A, B) = d = \sqrt{(x_2 - x_1)^2+ (y_2 - y_1)^2}$

Here in this problem,

$x_1 = 2 ; y_1 = -1 ; x_2 = -4 ; y_2 = 2$

Substituting the values in given formula, we get

$d = \sqrt{(-4-2)^2+(2-(-1))^2}\\\\d = \sqrt{(-6)^2 + (3)^2}\\\\d = \sqrt{36 + 9}\\\\d = \sqrt{45}$

On simplification we get,

$d = \sqrt{45} = \sqrt{3 \times 3 \times 5}\\\\d = 3\sqrt{5}$

Thus the distance between two points A(2, -1) and B(-4, 2) is $3 \sqrt{5}$ units