Question 7 of 50beginner💡 UnderstandVery Short1 mark

As you move away from segment AB along its perpendicular bisector, do the radii of the circles containing A and B increase or decrease?

Correct Answer

Increase

Exercise: Think and Reflect | Q: 3 | (Page 4)
For More Understanding

Explanation

According to the provided context, the centres of all circles passing through points A and B lie on the perpendicular bisector of AB, as every point on this bisector is equidistant from A and B. The radius of any such circle is the distance from its centre (a point on the perpendicular bisector) to point A. As you move further away from the segment AB along its perpendicular bisector, the distance from the centre to point A increases. Consequently, the radii of the circles containing A and B also increase.

Solution Steps

  1. Step 1: Identify that the centres of all circles passing through A and B lie on the perpendicular bisector of AB.

  2. Step 2: Recognize that the radius of such a circle equals the distance from the centre (on the perpendicular bisector) to point A.

  3. Step 3: Conclude that moving away from segment AB along the perpendicular bisector increases the distance to A, hence the radii increase.

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