Question

victor is making a perpendicular segment in the middle of segment xy . first, he drew an arc centered at x . then, he used the same radius to draw an arc centered at y . next, he found the points where the arcs intersected. what must be true?

Answer 1

Victor is using a compass construction method to create a perpendicular bisector of segment XY. The intersection points of the arcs he draws should be equidistant from X and Y to ensure the line drawn through them bisects XY at the midpoint and is perpendicular.

Step-by-step explanation:

Victor is attempting to create a perpendicular bisector of segment XY. The steps he has taken so far indicate the classical compass construction method. By drawing arcs with the same radius centered at both X and Y, and identifying the points where these arcs intersect, Victor can draw a line between these intersection points to form a perpendicular bisector of XY. For his construction to be accurate, it must be true that the arc intersections are equidistant from X and Y, thereby ensuring the bisector is both perpendicular to XY and bisects XY at its midpoint.

Answer 2

The statement that MUST be true is:

Any point on MN will be equidistant from X and Y.

Why the statement is true

Victor drew arcs with the same radius centered at X and Y. This ensures that the arcs have the same length and sweep out the same angle.

The arcs intersect at points M and N. These points are equidistant from the centers X and Y (since they are on the same arc with the same radius).

MN connects the intersection points. This creates a perpendicular bisector of XY.

Perpendicular bisectors have the property that any point on them is equidistant from the endpoints of the segment they bisect. This is a geometric theorem.

Therefore, based on the given information, we can conclude that any point on MN will be the same distance from X and Y.

Victor is making a perpendicular segment in the middle of segment XY . First, he drew an arc centered at X . Then, he used the same radius to draw an arc centered at Y . Next, he found the points where the arcs intersected. What MUST be true? A line goes from point X to point Y. Points M and N are on each side of the line. Arcs go from point M to point N. CLEAR CHECK M is the same distance from N as X is from Y . Any point on MN will be equidistant from X and Y . NY is half of XY . XY is equal to MN .