Answer: The correct option is (C) 2√34.
Step-by-step explanation: We are given to find the distance between the points (-2, 4) and (4, -6).
We have the distance formula as follows :
DISTANCE FORMULA :
The distance between the points (a, b) and (c, d) is given as
[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]
Therefore, the distance between the points (-2, 4) and (4, -6) is given by
[tex]D\\\\=\sqrt{(4-(-2))^2+(-6-4)^2}\\\\=\sqrt{6^2+10^2}\\\\=\sqrt{36+100}\\\\=\sqrt{136}\\\\=\sqrt{4\times34}\\\\=2\sqrt{34}.[/tex]
Thus, the required distance between the given points is 2√34 units.
Option (C) is CORRECT.
