I have a test today in this geometry course, and this was on our review sheet if you could please help me out with this question it would be very helpful thank you
Distance in $\mathbb{R^3}$ from points $P=(x_1, y_1, z_1)$ and $Q=(x_2, y_2, z_2)$ is given by $|PQ| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$
b) Describe the set of points equidistant to two points in $\mathbb{R^3}$. (So i tried to give this a try, and i said it would be a line but it doesnt make sense for some reason
c) Show that an isometry of $\mathbb{R^3}$ is determined by where it sends 4 points $A, B, C, D$ as long as $A, B, C, D$ are not coplanar (Hint:Do not lay on a single plane in $\mathbb{R^3}$)
A reflection in $\mathbb{R^3}$ is in a plae, for example, the reflection in in the $xy$-plane is given by
$r_{xy}(x, y, z) = (x, y, -z)$.
e) Show that any isometry of $\mathbb{R^3}$ is the composition of up to four reflections. A reflection in $\mathbb{R^3}$ is in a plane.
f)A screw transformation is a rotation about a line followed by a translation along that line ( think of turning a screw!) describe the reflections needed to produce a screw transformation alone a line $L \subset \mathbb{R^3}$. (I have no clue what this is talking about)
