Ruler and Compass Constructions: Practice Questions

A point \(P\) moves such that it is always at a constant distance of \(4\text{ cm}\) from a fixed point \(O\). Which of the following describes the locus of \(P\)?

Two parallel lines \(L_1\) and \(L_2\) are \(8\text{ cm}\) apart. A point \(P\) moves such that it is always equidistant from \(L_1\) and \(L_2\). Another point \(Q\) moves such that it is at a constant distance of \(3\text{ cm}\) from a point \(O\) located on \(L_1\). How many points satisfy both conditions for \(P\) and \(Q\)?

In a plane, point \(A\) and point \(B\) are \(6\text{ cm}\) apart. The locus of point \(P\) moves such that the area of \(\triangle PAB\) is always \(12\text{ cm}^2\). Which of the following best describes the locus of \(P\)?

In the figure, \(L\) is the perpendicular bisector of the line segment joining points \(A\) and \(B\). If a point \(X\) lies on \(L\), which of the following must be true?

A point \(P\) moves in a plane such that it maintains a constant distance of \(5\text{ cm}\) from a fixed point \(O\). Simultaneously, another point \(Q\) moves such that it is equidistant from two parallel lines \(L_1\) and \(L_2\) which are \(6\text{ cm}\) apart. If the point \(O\) lies on \(L_1\), how many points of intersection are there between the locus of \(P\) and the locus of \(Q\)?

Consider two fixed points \(A\) and \(B\) that are \(8\text{ cm}\) apart. A point \(P\) moves such that it is always equidistant from \(A\) and \(B\). A second point \(Q\) moves such that it maintains a constant distance of \(3\text{ cm}\) from the midpoint of \(AB\). Describe the geometric shape of each locus and determine how many points of intersection exist between the locus of \(P\) and the locus of \(Q\).