The co-ordinate diagram below shows two points A and B - Leaving Cert Mathematics - Question (iii) - 2021

Identify Points A and B: Locate points A and B on the coordinate diagram.

Determine the Center of the Circle: The center of the circle will be the midpoint of the line segment AB. Calculate the coordinates of the midpoint M using the formula:

$M = \left( \frac{x_A + x_B}{2}, \frac{y_A + y_B}{2} \right)$

Find the Radius: The distance from the center M to either point A or B will be the radius. Use the distance formula:

$r = \sqrt{(x_B - x_M)^2 + (y_B - y_M)^2}$.

Set the Compass: Adjust the compass to the length of the radius found in step 3.

Draw the Circle: Place the point of the compass on point M and draw a circle around it, ensuring that it passes through both points A and B.