Find the distance between the points (-2, 4) and (4, -6).

Solution:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by the relationship:

Distance between the two points = \(\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2}}\)

= \(\sqrt{(-2-(4))^{2} + (4-(-6))^{2}}\)

= \(\sqrt{(-6)^{2} + (10))^{2}}\)

= \(\sqrt{36 + 100}\)

= √136

= 2√34

Find the distance between the points (-2, 4) and (4, -6).

Summary:

The distance between the points (-2, 4) and (4, -6) is 2√34.