LOCUS AND CONSTRUCTION
Question 1
A particular P moves between S and T such that the angle SPT is always constant. Find the locus of P (UME 2007 Question 43)
A. It is a semicircle with ST as diameter
B. It is a perpendicular bisector of ST
C. It is a quadrant of a circle with ST as diameter
D. It is a diameter line perpendicular ST
Answer
Option A (Angle in a semicircle is 90)
Question 2
What is the locus of the point equidistant from (UME 2006, Question 33)
A. A line
B. A line
C. A line
D. A line
Answer Option A
Reason
For a point P to be equidistant from the point A and B,
its locus is the perpendicular bisector of the line AB (that is )
Question 3
Two lines PQ and ST intersect at 75o The locus of the point equidistant from PQ and ST lies on the (UME 2005 Question 31)
A. Perpendicular bisector of PQ
B. Perpendicular bisector of ST
C. Bisector of the angle between lines PQ and ST
D. Bisector of the angle between lines PT and QS
Answer: Option C
Question 4
The locus of a point, which is 5cm from the line LM, is a ________ (UME 2004 Question 30)
A. Pair of lines on opposite sides of LM and parallel to it.
B. Line parallel to LM and 5cm from LM
C. Pair of parallel lines on one side of LM and parallel to LM
D. Line distance 10cm from LM and parallel to LM
Answer option B
Question 5
The locus of a point P which moves on one side only of a straight XY so that
A. A circle
B. A semicircle
C. An arc of a circle of a circle through X, Y
D. The perpendicular bisector of XY
Answer option B
Reason:
Angle subtend in a semicircle on the circumference is always 90o
Question 6
The locus of a point P which is equidistant from two given point S and T is
A. The perpendicular bisector of ST
B. The angle bisector of PS and ST
C. A perpendicular to ST
D.
A
line parallel to ST
Answer Option A
Question 7
A point P moves such that it is equidistant from point Q and R. Find QR when PR = 8cm and <PRQ = 30o (UME 2001,Question 26)
Solution
Note: the locus of a point P which is equidistant from two given point Q and R is the perpendicular bisector of QR.
Question 8
Find the locus of a point such that its distance from the line y = 4 is a constant (UME 2001, Question 27)
A.
B.
C.
D.
Answer: option D
Reason: Point P must be a constant perpendicular distant AB, It may lie on either sides of the line y = 4 and placed at equal distance say k.
Question 9
Find the equation of the locus of a point P(x,y) such that PV = PW when V=(1,1) and W(3,5) (UME 1999, Question 30)
Solution
Solution
Question 10
A point P moves so that it is equidistant from point L and M if LM is 16cm. Find the distance of P from LM, when P is 10cm from L (UME 1997, Question 32)
Solution
Using Pythagoras theorem
The distance of P from LM is 6cm.
Question 11
P is on the locus point equidistant from two given point X and Y, UV is a straight line through Y parallel to the locus if is 40o. Find
Solution
Since P is equidistant from point X and point Y, XP =YP
Question 12
What is the locus of a point P which moves on one side of a straight line XY, so that angle XPY is always equal to 90o ?
A. The perpendicular bisector of XY
B. A right –angled triangle
C.
A circle
D. A semicircle
Answer: Option D
Question 13
The locus of point which is equidistant from two given fixed point is the (UME 1992, Question 31)
A. A perpendicular bisector of the straight line joining them
B. Parallel line to the straight line joining them
C. Transverse to the straight line
D. Angle bisector of 90o, which the straight line joining them make with the horizontal
Answer: Option A
Question 14
The locus of a point which moves so that it is equidistant from two intersecting straight lines is the (UME 1991, Question 45)
A. Perpendicular bisector of the two lines
B. Angle bisector of the two lines
C. Bisector of the two lines
D.
Line parallel to the two lines
Answer: Option B
Question
PQR is a triangle in which PQ =10cm and =60o. S is a point equidistant from P and Q, also S is appoint equidistant from PQ and PR. If U is the foot of the perpendicular from S on PR. Find the length SU in cm to 1decimal place. (UME 1988, Question 46)
Solution
Question
The figure above is an example of a construction of a ( UME 1987, Question 44)
A. Perpendicular bisector of a given straight line
B. Perpendicular from a given point to a given line
C. Perpendicular to a line from a given point on that line
D. Given angle
Answer: Option A
Question 15
What is the locus of the mid –points to all chords of length 6cm within a circle of radius 5cm and with center O? ((UME 1987 Question 45)
A. A circle of radius 5cm and with center O
B. The perpendicular bisectors of the chords
C. The straight line passing through center O
D. A circle of radius 6cm with center O
Answer Option B
Question 16
If U and V are two distinct fixed points and W is a variable points such that UWV is a right angle, what is the locus of W. (UME 1986, Question 42)
A. The perpendicular bisector of UV
B. A circle with UV as radius
C. A line parallel to the line UV
D. A circle with line UV as the diameter
Answer Option D
Question 17
Use
the construction below to answer question i and ii (UME 1984,
Question 48 & 50)
i. What is the obtuse angle formed when the point U is joined o
A 75o B. 145o C. 120o D. 105o E. 125o
Answer Option D
Reason: The angle form when point S is joined to point O is 120o. The angle formed when point T is joined to O is 90o. Point U joined to O is the bisector of angle formed when point S and T is joined to point O i.e
ii What is the angle formed when the point V is joined to point O?
A 60o B. 30o C. 45o D. 90o E. 15o
Answer Option B
Question 18
The locus of all points having a distance of l units from each of two fixed points a and b is (UME 1979, Question 40)
A. A line parallel to the line ab
B. A line perpendicular to the line ab through mid-point of ab
C. A circle through a and b with center at the mid point of ab
D. A circle with center at a and passes through b
Answer: Option B
Question 19
P
and Q are fixed point and X is a variable point which moves so that angle .What
is the locus of X (UME 1980, Question 16)
A. A pair of straight line parallel to PQ
B. The perpendicular bisector of PQ
C. An arc of a circle passing through P and Q
D. A circle with diameter PQ
E. The bisector of angle PQ
Answer: Option C
Question 20
Find the equation of the set of points, which are equidistant from the parallel line x =1 and x = 7,
A. y = 3 B. x =3 C. x = 4 D. y = 4
Answer:
Option C
Question 21
The locus of a point equidistant from two points P(6,2) and R(4,2) is a perpendicular bisector PR
(a) (2,3) (b) (5,2) (c) (1,0) (d) (0,1)
(
Solution
The midpoint of P and R is
Answer: Option B
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