Construct triangle ABC.

• Draw a line segment BC of length $10 \text{ cm}$.
• At point C, construct an angle of $60^\circ$. To do this:
  • Place the compass at C and draw an arc that intersects BC.
  • Without changing the compass radius, place the compass at the intersection point on BC and draw another arc that intersects the first arc.
  • Draw a ray from C through this intersection point. This ray forms a $60^\circ$ angle with BC.
• At point B, construct an angle of $45^\circ$. To do this:
  • First, construct a $90^\circ$ angle at B. Extend BC to the left. Place the compass at B and draw an arc intersecting the line at two points. From these two points, draw arcs above B that intersect. Draw a ray from B through this intersection point to form a $90^\circ$ angle with BC.
  • Bisect the $90^\circ$ angle. Place the compass at B and draw an arc intersecting the $90^\circ$ ray and BC. From these two intersection points, draw arcs that intersect within the angle.
  • Draw a ray from B through this intersection point. This ray forms a $45^\circ$ angle with BC.
• The intersection of the $60^\circ$ ray from C and the $45^\circ$ ray from B is point A.

This is the perpendicular bisector of the line segment BC.

• Place the compass at B and open it to a radius greater than half the length of BC. Draw arcs above and below BC.
• Without changing the compass radius, place the compass at C and draw arcs that intersect the previous arcs.
• Draw a straight line connecting the two intersection points of the arcs. This line is Locus X.

We interpret "1/2 of points from A" as the locus of points at a distance of half the length of BC from A.

• Calculate the radius: $R = \frac{1}{2} \times BC = \frac{1}{2} \times 10 \text{ cm} = 5 \text{ cm}$.
• Set the compass to a radius of $5 \text{ cm}$.
• Place the compass point at A.
• Draw a circle. This circle is Locus Y.

• The points where the perpendicular bisector (Locus X) intersects the circle (Locus Y) are the required points of intersection. Mark these points.