**9.2.1 Loci in Two Dimensions, PT3 Focus Practice**

**Question 1:**

Diagram below in the answer space shows a square

*PQRS*with sides of 6 units drawn on a grid of equal squares with sides of 1 unit.*W*,*X*and*Y*are three moving points inside the square.*W*is the point which moves such that it is always equidistant from point

*P*and point

*R*. (a)

By using the letters in diagram, state the locus of

*W*. (b) On the diagram, draw,

*X*which moves such that it is always equidistant from the straight (i) the locus of the point lines

*PQ*and

*PS*,

*Y*which moves such that its distance is constantly 2 units from point (ii) the locus of the point

*K*.

*X*and the locus of

*Y*. (c) Hence, mark with the symbol ⊗ the intersection of the locus of

AnswerAnswer

**:**

(b)(i),(ii)

*Solution***:**

**(a)**

*QS*

(b)(i),(ii)

(b)(i),(ii)

**(c)**

**Question 2:**

Diagram in the answer space below, shows a regular pentagon

*PQRST*.*W*,*X*and*Y*are moving points which move in the pentagon.On the diagram,

*W*which moves such that it is always equidistant from point

*R*and

*S*. (a) draw the locus of the point

*X*which moves such that

*XR*=

*RS*. (b) draw the locus of the point

*Y*which moves such that its distance is constantly 3 cm from the line

*SR*. (c) draw the locus of point

*W*and the locus of

*X*. (d) hence, mark with the symbol ⊗ the intersection of the locus of

AnswerAnswer

**:**

(a), (b), (c) and (d)

*Solution***:**

**(a), (b), (c) and (d)**

**Question 3:**

Diagram in the answer space below shows a polygon.

*X*and

*Y*are two moving points in the polygon.

(a) On the diagram, draw

(i) the locus of the point

*X*such that

*XQ*=

*XR*.

(ii) the locus of the point

*Y*such that

*YQ*=

*QR*.

(b) Hence, mark with the symbol $\otimes $ the intersection of the locus of

*X*and the locus of

*Y*.

*Answer***:**

(a)(i), (ii) and (b)

*Solution***:**