Question

Help me plz asap so i can make dinner im starving but i can start till i finish

Answer 1

A.) They are the same.

Step-by-step 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) =
`\sqrt{\mathbf{(x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)}}`

distance(FO) =
`\sqrt{(4-(-3))^(2)+(0-2)^(2)}` =
`\sqrt{(7)^(2)+(-2)^(2)}` =
`√(49+4)` =
`√(53)`

distance(FG) =
`\sqrt{(4-(-3))^(2)+(0-(-2))^(2)}` =
`\sqrt{(7)^(2)+(2)^(2)}` =
`√(49+4)` =
`√(53)`

Therefore distance(FO) = distance(FG) =
`\sqrt{\mathbf{53}}`

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)