Question

willhite_k. geometry a_section 1_fall 25/26 / unit 5 - triangle properties
what is the name of the figure described?
the locus of points in a plane equidistant from endpoints d and e.
two lines parallel to line m and each 5 inches from m on either side of it.
a line perpendicular to line m.
the perpendicular bisector of \\( \overline { d e } \\).
\\( \overline { d e } \\)

1. choose the correct answer.

what is the name of the figure described?
all points in a plane 5 inches from line m.
a line perpendicular to line m.
two lines parallel to line m and each 5 inches from m on either side of it.
the perpendicular bisector of \\( \overline { d e } \\).

Explanation:

• For the first question: By the definition of the perpendicular bisector of a segment, the locus of points in a plane equidistant from endpoints \(D\) and \(E\) is the perpendicular bisector of \(\overline{DE}\).
• For the second question: The set of all points in a plane at a fixed distance (5 inches) from a given line \(m\) forms two lines parallel to \(m\) (one on each side of \(m\)) at that distance.

Answer:

• First question: The perpendicular bisector of \(\overline{DE}\).
• Second question: Two lines parallel to line \(m\) and each 5 inches from \(m\) on either side of it.