Question

7 practice 7 (from unit 1, lesson 3)
here are 2 points in the plane.
explain how to construct the set of all points that are equidistant from point e and point f.

Explanation:

Step1: Recall geometric property

The set of points equidistant from two points is the perpendicular bisector of the line - segment joining them.

Step2: List construction steps

1. Use a straight - edge to draw the line segment $\overline{EF}$.
2. Place the compass at point $E$ and set the width of the compass to a length greater than $\frac{1}{2}EF$.
3. Draw arcs above and below the line segment $\overline{EF}$.
4. Without changing the compass width, place the compass at point $F$ and draw arcs above and below the line segment $\overline{EF}$, intersecting the previous arcs at two points, say $A$ and $B$.
5. Use a straight - edge to draw the line passing through points $A$ and $B$. This line is the perpendicular bisector of $\overline{EF}$, and all points on this line are equidistant from $E$ and $F$.

Answer:

Construct the perpendicular bisector of the line segment $\overline{EF}$ using a compass and straight - edge as described above. The perpendicular bisector is the set of all points that are equidistant from point $E$ and point $F$.