Name: __________________________ Class: __________( ) Prepared by B Lo

Lesson Worksheet 8B (Refer to Book 1B 8.2)

8.2 Distance between Two Points

(a) For points lying on a horizontal line, y

they have the same y-coordinate.
(b) For points A(a , k) and B(b , k) on a B(b , k) A(a , k)
horizontal line, where a > b, the x
O
distance between A and B is given by
AB = a – b.

1. Refer to the figure. Find the distance between C and D. y

C(2 , 4) D(10 , 4) Check if
CD is a
Check if
horizontal
CD is a
line.
x horizontal
O line.

Practice
2. Refer to the figure. Find the distance between 3. Find the length of the line segment RS in
P and Q. the figure. It means ‘the distance
y between R and S’.
y
x
O
P(–8 , 4) Q(–1 , 4) R(– 4 , –2) S(7 , –2)

x
O

(a) For points lying on a vertical line, y

they have the same x-coordinate. P(h , p)
x
(b) For points P(h , p) and Q(h , q) on O
a vertical line, where p > q, the Q(h , q)
distance between P and Q is given by
PQ = p – q.

S1 Mathematics Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo

4. Refer to the figure. Find the distance between P and Q. y

P(5 , 4)

Q(5 , 1)
x
O

Practice
5. (a) Find the lengths of AB and CD in the figure.
(b) Hence, determine which line segment, AB or CD, is shorter.
y
x
O
A(– 4 , –1)

C(1 , –5)
D(–6, –5)
B(– 4 , –7)

6. Find the distance between

Do the two points
(a) M(3 , 5) and N(3 , 11), lie on a horizontal
or vertical line?
(b) U(6 , 8) and V(7 , 8).

S1 Mathematics 2 Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo
Practice
7. Find the distance between
(a) E(4 , 7) and F(5 , 7),
(b) G(2 , 0) and H(9 , 0).

Practice
8. Given that the distance between points P and 9. Given that the distance between points R
Q in the figure is 7 units, find the value of a. and S in the figure is 10 units, find the value
y of d.
P(2 , 4) Q(a , 4) Is PQ horizontal? y
Why? R(11 , 4)
7 units
x x
O O 10 units

S(11 , d)

S1 Mathematics 3 Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo
10. The figure shows a rectangle ABCD, whose sides are either horizontal or vertical.
(a) Find the coordinates of B. y
(b) Find the perimeter of rectangle ABCD. A(1 , 5) B

D C(8 , 2)
x
O

Practice
11. The figure shows a rectangle PQRS, whose sides are either y
x
horizontal or vertical. O
P(–8 , –2) Q
(a) Find the coordinates of S.
(b) Find the perimeter of rectangle PQRS.

S R(–2 , –7)

S1 Mathematics 4 Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo
12. A(–1 , 5) and B(3 , 5) are two points in a rectangular coordinate plane.
(a) Determine whether line AB is horizontal or vertical.
(b) Find the length of AB.
(c) C is another point lying on the line AB such that AB = BC. Find the coordinates of C.

S1 Mathematics 5 Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo
Practice
13. S(6 , 1) and T(2 , 1) are two points in a rectangular
Step : Sketch the points S and T.
coordinate plane. Then draw a straight line ST.
(a) Determine whether line ST is horizontal or vertical. Step : Locate point U on the line
drawn such that ST = TU.
(b) Find the length of ST. y
(c) U is another point lying on the line ST such that
ST = TU. Find the coordinates of U.
x
O

14. C(1 , 3) and D(d , 3) are two points in a rectangular coordinate plane. If CD = 6 units, find the two
possible values of d.

S1 Mathematics 6 Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo
Practice
15. A(3 , 1) and B(b , 1) are two points in a rectangular coordinate plane. If AB = 8 units, find the
two possible values of b.
y

x
O
A(3 , 1)

Practice
16. J(1 , 2) and L(7 , 5) are two vertices of a rectangle JKLM, where JK is horizontal. Is JKLM a
square? Explain your answer. Check if the sides of rectangle JKLM
are equal.

S1 Mathematics 7 Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo
Practice
17. The figure shows a polygon ABCDEF, whose sides are either y
horizontal or vertical. F(2 , 4) A
(a) Find the coordinates of A, C and E.
C B(3 , 1)
(b) Find the perimeter of polygon ABCDEF.
x
O

E D(1 , 2)

S1 Mathematics 8 Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo
Practice
18. A(3 , – 2) is a point in a rectangular coordinate plane. If AB is either horizontal or vertical, and
AB = 4 units, find two of the possible coordinates of B.
B can be lie above/below/ y
on the left of/on the right
of A. Locate two of them in
the figure. x
O
A(3 , 2)

S1 Mathematics 9 Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo
Level 3
19. (Q26 of 8B) EFGH is a square, where EF and HG are horizontal. The coordinates of E are (4 , –3)
and the perimeter of EFGH is 24 units. If all the sides of EFGH do not intersect the x-axis nor the
y-axis, find the coordinates of F, G and H.

S1 Mathematics 10 Topic 8 Rectangular Coordinate System (I)

 Prepared by B Lo
20. (Q27 of 8B) The figure shows a polygon ABCDEFGH, whose
sides are either horizontal or vertical. Find the perimeter of
ABCDEFGH.

S1 Mathematics 11 Topic 8 Rectangular Coordinate System (I)