8.2.2 Loci in Two Dimensions, PT3 Focus Practice


8.2.2 Loci in Two Dimensions, PT3 Focus Practice

Question 3:
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.

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


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

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



Question 4:
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.

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


Solution
:

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