Question 1 of 11intermediate🔍 AnalyzeShort Answer2 marks

When constructing the perpendicular bisector, is it necessary to have the same radius for the arcs above and below XY? Explore this through construction, and then justify your answer.

Correct Answer

No, it is not necessary to have the same radius for the arcs above and below XY.

Reasoning: The perpendicular bisector is determined by any two points that are equidistant from both X and Y. As long as the arcs from X and Y intersect at a point (whether above or below XY), that intersection point lies on the perpendicular bisector. Different radii can be used for the upper and lower arc pairs. The line joining any two such intersection points will still be the perpendicular bisector of XY.

Justification: Any point that has the same distance from X and Y lies on the perpendicular bisector of XY. When constructing arcs from X and Y with the same radius, the intersection point is equidistant from both X and Y. The perpendicular bisector can be drawn if any two points on it are known. ∴ Even if different radii are used for the upper and lower arc pairs, each intersection point still lies on the perpendicular bisector, and joining any two such points gives the perpendicular bisector.

Exercise: Figure it Out (Section 1) | Q: 1 | (Page Page 5)
For More Understanding

Explanation

The chapter explains that any point that has the same distance from X and Y lies on the perpendicular bisector of XY. When constructing arcs from X and Y with the same radius, the intersection point is equidistant from both X and Y. The perpendicular bisector can be drawn if any two points on it are known. Therefore, even if different radii are used for the upper and lower arc pairs, each intersection point still lies on the perpendicular bisector, and joining any two such points gives the perpendicular bisector.

Solution Steps

  1. Understand that the perpendicular bisector is determined by any two points equidistant from both X and Y.

  2. Recognize that intersection points of arcs from X and Y lie on the perpendicular bisector.

  3. Note that different radii can be used for upper and lower arc pairs.

  4. Conclude that joining any two intersection points gives the perpendicular bisector.

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