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

Question 4:

Question 4:

Diagram below in the answer space shows a quadrilateral

*ABCD*drawn on a grid of equal squares with sides of 1 unit.*X*,

*Y*and

*Z*are three moving points inside the quadrilateral

*ABCD*.

*X*is the point which moves such that it is always equidistant from point

*B*and point

*D*. (a)

By using the letters in diagram, state the locus of

*X*.(b) On the diagram, draw,(i)

*Y*such that it is always 6 units from point

*A*,

the locus of the point (ii)

*Z*which moves such that its distance is constantly 3 units from the the locus of the point

line

*AB*.

*Y*and the locus of

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

AnswerAnswer

**:**

(b)(i),(ii) and (c)

SolutionSolution

**:**

**(a)**The locus of

*X*is the line

*AC*.

(b)(i),(ii) and (c)

(b)(i),(ii) and (c)

**Question 5:**

Diagram in the answer space below shows a square

*ABCD*.*E*,*F*,*G*and*H*are the midpoints of straight lines*AD*,*AB*,*BC*and*CD*respectively.*W*,*X*and*Y*are moving points in the square.On the diagram,

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

*AD*and

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

*X*which moves such that

*XM*=

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

*Y*which moves such that its distance is constantly 6 cm from point

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

*W*and the locus of

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

AnswerAnswer

**:**

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

SolutionSolution

**:**

**Question 6:**

Diagram in the answer space below shows a polygon

*ABCDEF*drawn on a grid of squares with sides of 1 unit.

*X, Y*and

*Z*are the points that move in the polygon.

(a)

*X*is a point which moves such that it is equidistant from point

*B*and point

*F*.

By using the letters in diagram, state the locus of

*X*.

(b) On the diagram, draw

(i) the locus of the point

*Y*which moves such that it is always parallel and equidistant from the straight lines

*BA*and

*CD*.

(ii) the locus of point

*Z*which moves such that its distance is constantly 6 units from the point

*A*.

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

*Y*and the locus of

*Z*.

*Answer***:**

(b)(i), (ii) and (c)

*Solution***:**

**(a)**The locus of

*X*is

*AD*.

**(b)(i),(ii) and (c)**