Locus- (11.1-11.3)

Understand the concept of loci

• In geometry, a locus is a set of points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

Describe and sketch the locus of points satisfying given conditions

• Square ABCD is rotated about its vertex C. Sketch and describe the locus of vertex A.

• The locus of B is a circle with the centre at D and BD as its radius.

Describe the locus of points with algebraic equations

• It is given that a moving point P is equidistant from A(-2, 0) and B(3,-5).
(a) Draw and describe the locus of P.
(b) Find the equation of the locus of P.

• (a) The locus of P is the perpendicular bisector of AB.

(b) Let (x, y) be the coordinates of the moving point P.
$$AP = \sqrt {{{[x - ( - 2)]}^2} + {{(y - 0)}^2}}$$ units
$$= \sqrt {{{(x + 2)}^2} + {y^2}}$$ units

$$BP = \sqrt {{{(x - 3)}^2} + {{[y - ( - 5)]}^2}}$$ units
$$= \sqrt {{{(x - 3)}^2} + {{(y + 5)}^2}}$$ units
Therefore, the equation of the locus of P is $$x - y - 3 = 0$$.