# 9.2.2 Loci in Two Dimensions, PT3 Focus Practice

9.2.2 Loci in Two Dimensions, PT3 Focus Practice

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.
(a) X is the point which moves such that it is always equidistant from point B and point D.
By using the letters in diagram, state the locus of X.
(b) On the diagram, draw,
(i) the locus of the point Y such that it is always 6 units from point A,
(ii) the locus of the point Z which moves such that its distance is constantly 3 units from the
line AB.
(c) Hence, mark with the symbol ⊗ the intersection of the locus of Y and the locus of Z.

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

Solution
:
(a) The locus of X is the line AC.

(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,
(a) draw the locus of the point W which moves such that it is always equidistant from point AD and BC.
(b)   draw the locus of the point X which moves such that XM = MG.
(c) draw the locus of point Y which moves such that its distance is constantly 6 cm from point C.
(d)   Hence, mark with the symbol ⊗  the intersection of the locus of W and the locus of Y.

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

Solution
:

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.