Answer :
The distance between two points A(2, -1) and B(-4, 2) is [tex]3 \sqrt{5}[/tex] 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 [tex]A(x_1, y_1)[/tex] and [tex]B(x_2, y_2)[/tex] is given as:
[tex]Distance(A, B) = d = \sqrt{(x_2 - x_1)^2+ (y_2 - y_1)^2}[/tex]
Here in this problem,
[tex]x_1 = 2 ; y_1 = -1 ; x_2 = -4 ; y_2 = 2[/tex]
Substituting the values in given formula, we get
[tex]d = \sqrt{(-4-2)^2+(2-(-1))^2}\\\\d = \sqrt{(-6)^2 + (3)^2}\\\\d = \sqrt{36 + 9}\\\\d = \sqrt{45}[/tex]
On simplification we get,
[tex]d = \sqrt{45} = \sqrt{3 \times 3 \times 5}\\\\d = 3\sqrt{5}[/tex]
Thus the distance between two points A(2, -1) and B(-4, 2) is [tex]3 \sqrt{5}[/tex] units