review exercise 21 (subjective)

8/18/2019 Review Exercise 21 (Subjective)

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Review Exercise 21

Subjective Questions

1. State the locus of the tip of a pencil that moves in the following situations.

(a) (b)

(c) (d)

2. The diagram shows weighing scales. When some fish are placed on the

weighing scales, state the locus of

(a) the tip of the pointer P ,(b) the corner of the plate Q.

3.

In the diagram, EF is a line segment. Determine the locus of a point that moves on a plane such that its distances from E and F are equal.

© Pearson Malaysia Sdn. Bhd. 2008 Essential Mathematics PMR1

E

F


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Review Exercise 21

4.

The diagram shows an equilateral triangle EFT . A, B and C are the midpoints of EF ,

FG and GE respectivel. State the locus of a point P that moves inside the triangle

EFG under the following conditions.

(a) The distances of P from E and F are equal.(b) The perpendicular distances of P from EF and EG are equal.

(c) The perpendicular distances of P from FG and FE are equal.

(d) The distance of P from G is!

"GF .

5. XYZW is a rhombus with sides of length # cm. $ point S moves inside the rhombus

XXZW . State the locus of the point S such that

(a) SY % SW .

(b) the perpendicular distance of S from XY is ! cm.

6.

In the diagram, GHIJ is a trape&ium. $ point R moves inside the trape&ium GHIJ .

State the locus of the point R such that

(a) its distances from I and J are equal.

(b) its distances from GH and GJ are equal.


J

I

G H

G

F E

BC

A


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Review Exercise 21

7.

In the diagram, GHS is an equilateral triangle with sides of length ' cm. $ point W

moves inside the triangle GHS such that OW % " cm.

op the diagram and construct the locus of the point W .

8.

The diagram shows a rhombus EFGH with sides of length cm. $ point moves

inside the rhombus under the following conditions.

(a) The distances of the point Y from points E and H are equal.

(b) The perpendicular distance of the point Y from the diagonal FH is " cm.*n a separate diagram, construct each of the locus of the point Y .

9.

The diagram shows a triangle DEF . Draw the triangle DEF accuratel and construct

on it

(a) the locus of a point M that moves inside the triangle DEF such that

EM % # cm.(b) the locus of a point N that moves inside the triangle DEF such that DN % EN .


H G

E F

H

S

G

O

D

E F

cm

' cm

+-


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Review Exercise 21

10. In a triangle PQR, PQ % + cm, PR % ' cm and ∠ QPR % /-. T is a point that moves

inside the triangle PQR. *n a separate diagram, construct the locus of the point T if

(a) PT % # cm.

(b) the distance of T from QR is ! cm.

(c) the distances of T from the points Q and R are equal.(d) the distances of T from the sides PQ and PR are equal.

11.

In the diagram, A, O and B are points on a straight line.

onstruct, accuratel, the locus of

(a) the point that moves such that its perpendicular distance from the line AB is " cm,

(b) the point that moves such that its distance from the point O is ! cm.

0ind the points of intersection of the two loci.

12.

(a) *n the graph, construct the locus of (i) the point P that moves on the artesian plane such that HP % # cm,(ii) the point Q that moves on the artesian plane such that HQ % MQ,

(iii) the point R that moves such that the perpendicular distance of R from the x1

a2is is " cm.

(b) (i) State the number of points that satisf the conditions of the locus

and the locus (a)(ii).


A ! cm # cmO B

3

!

! 34!

y

5


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Review Exercise 21

(ii) ar6 with the smbol ⊗ , all the points that satisf the conditions of the

locus (a)(i) and the locus (a)(iii).

13.

In the diagram, KMQ and KMP are two equilateral triangles with sides of length 'cm. KFM and PFQ are straight lines.

(a) $ point X moves inside the figure such that its perpendicular distances from KP

and MP are equal. 7 using the letters in the diagram, state the locus of the point

X .

(b) Two other points Y and Z move inside the figure such that KY % KF and the

perpendicular distance of the point Z from the straight line KFM is " cm.

onstruct the locus of the point Y and the locus of the point Z .

(c) ar6 with the smbol⊗ , all the points of intersection of the locus of the point

Y and the locus of the point Z .


Q

M K

P

0


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Review Exercise 21

14.

The diagram shows a regular he2agon ABCDEF with sides of length cm. G is the

midpoint of CF .

(a) $ point X moves inside the he2agon ABCDEF such that its perpendicular

distances from AB and AF are equal. Describe the locus of X .

(b) *n the diagram, construct the locus of the

(i) point Y that moves inside the he2agon ABCDEF such that its perpendicular

distance from the line AC is # cm.

(ii) point Z that moves inside the he2agon ABCDEF such that its distance from

the point G is # cm.(c) (i) State the number of points of intersection of the locus of X and the locus of

Y .

(ii) ar6 with the smbol ⊗ all the points that satisf the conditions of the

locus of Y and the locus of Z .



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Review Exercise 21

15. In the diagram, the x1a2is and the y1a2is are drawn on square grids with sides of

length " cm.

Three points X , Y and Z move inside the quadrilateral GHKP .

(a) onstruct the locus of the

(i) point X such that JX % ! cm.

(ii) point Y such that it is equidistant from the lines HG and HK .

(ii) point Z such that its perpendicular distance from the x1a2is is " cm.(b) (i) State the coordinates of all the points that satisf the conditions of the locus

Y and locus Z .

(ii) ar6 with the smbol ⊗ , all the points that satisf the conditions of locus

X and locus Z .


review exercise 21 (subjective)

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