check the picture below.
now, the distance form -4,2 to 2,2 you can pretty much get it off the grid by counting the units.
and the distance from 2,2 to 2, -1, you also can get it off the grid by just counting.
now, let's check the other lengths,
from -4, 2 to -5, -2
from -5, -2 to -2, -3
from -2, -3 to 2, -1
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -4}}\quad ,&{{ 2}})\quad % (c,d) &({{ -5}}\quad ,&{{ -2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=√([-5-(-4)]^2+[-2-2]^2)\implies d=√((-5+4)^2+(-4)^2) \\\\\\ d=√((-1)^2+(-4)^2)\implies d=√(1+16)\implies \boxed{d=√(17)}\\\\ -------------------------------]()
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (c,d) &({{ -5}}\quad ,&{{ -2}}) % (a,b) &({{ -2}}\quad ,&{{ -3}})\quad \end{array}\qquad \\\\\\ d=√([-2-(-5)]^2+[-3-(-2)]^2)\\\\\\ d=√((-2+5)^2+(-3+2)^2) \\\\\\ d=√(3^2+(-1)^2)\implies d=√(9+1)\implies \boxed{d=√(10)}\\\\ -------------------------------\\\\]()
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ -3}})\quad % (c,d) &({{ 2}}\quad ,&{{ -1}}) \end{array}\qquad \\\\\\ d=√([2-(-2)]^2+[-1-(-3)]^2)\implies d=√((2+2)^2+(-1+3)^2) \\\\\\ d=√(4^2+2^2)\implies d=√(16+4)\implies d=√(20)\implies \boxed{d=2√(5)}]()
