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### Question 8 Analysis

The question involves a geometric problem on a square grid with sides of 1 unit, where points \( A \), \( B \), and \( C \) move in the diagram.

1. **Part (a):**
   - Point \( A \) is always equidistant from lines \( PT \) and \( RS \).
   - We need to state the locus of point \( A \) based on this condition. The locus of a point equidistant from two lines is the bisector of the angle formed by those two lines.
   
   **Solution for (a):**
   - Identify the lines \( PT \) and \( RS \) in the diagram.
   - Find the angle bisector between these two lines to determine the locus of point \( A \). It will be a line.

2. **Part (b):**
   - (i) The locus of point \( B \) is such that its distance from point \( P \) is always 5 units.
     - This is a circle centered at \( P \) with a radius of 5 units.
   - (ii) The locus of point \( C \) is such that its distance from line \( RS \) is always 2 units.
     - This will be two lines parallel to \( RS \), 2 units above and below it.

   **Solution for (b):**
   - Draw the circle with center \( P \) and radius 5 units.
   - Draw the parallel lines that are 2 units away from \( RS \) on both sides.

3. **Part (c):**
   - Mark the intersection of the locus of point \( B \) (the circle) and the locus of point \( C \) (the parallel lines) with the symbol \( \otimes \).

   **Solution for (c):**
   - Identify the points where the circle and the parallel lines intersect, and mark the intersection.

### Steps:
- (a) Find the bisector for point \( A \).
- (b-i) Draw the circle for \( B \) around \( P \) with radius 5.
- (b-ii) Draw parallel lines to \( RS \) for \( C \).
- (c) Mark the intersection points of the circle and the lines.

Do you want more details or a further breakdown of the solution?

Here are five relative questions:
1. How is the locus of a point equidistant from two lines generally determined?
2. What is the geometric definition of the locus of points around a fixed center?
3. How do you construct a locus of points that maintain a fixed distance from a line?
4. How do loci of a circle and a pair of parallel lines intersect in geometric problems?
5. What happens if the radius of the circle changes in this type of geometric setup?

**Tip:** When dealing with loci involving distances from lines, always consider if the problem asks for a fixed or variable distance, as this determines whether the locus is a line or a set of parallel lines.

The diagram is drawn on a square grid with sides of 1 unit. A, B, and C are three points that move in the diagram.
(a) Point A moves such that it is always equidistant from lines PT and RS. State the locus of point A by using the letters in the diagram.
(b) On the diagram, draw
(i) the locus of point B such that its distance from point P is always 5 units.
(ii) the locus of point C such that its distance from line RS is always 2 units.
(c) Hence, mark the intersection of the locus of B and locus of C with the symbol ⊗.

Explore a geometric problem involving loci on a square grid. Learn how to determine the locus of a point equidistant from two lines, draw circles based on fixed distances, and intersect loci of parallel lines and circles. Suitable for Grades 9-12.

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