The distance between point F and point G is option 1. 4.5 units.
Step-by-step explanation:
Step 1:
First, we plot the points F and G.
The point F is at (-1, 6) and point G is at (3, 4).
To calculate the distance between these two points, we use the formula
[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}.[/tex]
Step 2:
Take point F as the first point and point G as the second point.
So [tex](x_{1}, y_{1}) = (-1, 6)[/tex] and [tex](x_{2}, y_{2}) = (3, 4).[/tex]
Substituting the values in the equation, we get
[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} =\sqrt{\left(3-(-1)}\right)^{2}+\left(4-6\right)^{2}}.[/tex]
[tex]\sqrt{\left(3-(-1)}\right)^{2}+\left(4-6\right)^{2}} = \sqrt{\left(4}\right)^{2}+\left(-2\right)^{2}}.[/tex]
[tex]\sqrt{\left(4}\right)^{2}+\left(-2\right)^{2}} = \sqrt{\left(16}\right)+\left(4\right)} = \sqrt{20} .[/tex]
[tex]\sqrt{20} = 4.4721.[/tex]
Rounding this off, we get that the distance between point F and point G is 4.5 units.
