Answer:
A.) They are the same.
Explanation:
Let us first assume the length of side of one square to be 1 unit.
Let us solve this question by coordinate geometry:
first get the position coordinates by assuming R as origin.
Therefore position coordinates of points are:
R(0,0) ; F(4,0) ; O(-3,2) ; G(-3,-2)
Distance between two points, namely A(x₁ , y₁) and B(x₂ , y₂), in coordinate system is given by:
distance(AB) = [tex]\sqrt{\mathbf{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}}[/tex]
distance(FO) = [tex]\sqrt{(4-(-3))^{2}+(0-2)^{2}}[/tex] = [tex]\sqrt{(7)^{2}+(-2)^{2}}[/tex] = [tex]\sqrt{49+4}[/tex] = [tex]\sqrt{53}[/tex]
distance(FG) = [tex]\sqrt{(4-(-3))^{2}+(0-(-2))^{2}}[/tex] = [tex]\sqrt{(7)^{2}+(2)^{2}}[/tex] = [tex]\sqrt{49+4}[/tex] = [tex]\sqrt{53}[/tex]
Therefore distance(FO) = distance(FG) = [tex]\sqrt{\mathbf{53}}[/tex]
Hence the distance from F to O and G are equal.
(NOTE: In Z(x,y), x is the horizontal distance in units between Z and origin, if Z is on the left side of origin then distance is treated as positive and if the point is on the right side of origin then distance is treated as negative, y is the vertical distance between Z and origin, if Z above origin then y is positive and if point is below origin then y is negative but still magnitude of y will be the distance)
