Rectangular Coordinate System (I) 8.63
Level 2
25. The figure shows three points A, B and C lying on a straight
line. If the x-coordinate and y-coordinate of each of the points
A, B and C are interchanged, three new points P, Q and R are
obtained respectively.
(a) Plot the points P, Q and R in the figure. Do P, Q and R lie
on the same straight line?
(b) Among the points A, B, C, P, Q and R, how many points lie
above the x-axis?
26. (a) Plot the following points in a rectangular coordinate plane:
D(-4 , 5), E(-8 , 1), F(-4 , -5) and G(4 , 1).
(b) Join DE, EF, FG and GD.
(c) (i) Draw the two diagonals of quadrilateral DEFG. Are they
perpendicular to each other?
(ii) Find the coordinates of the point of intersection of the two
diagonals of DEFG.
27. H(h , 3.5) and K(4 , 3.5) are two points in a rectangular coordinate
plane.
(a) Determine whether HK is a horizontal line or a vertical line.
(b) It is given that HK = 6 units. Find the two possible values of h.
28. In the figure, OEFG is a square while OGH is a right- angled
triangle. OG = x units, GH = (x + 1) units and OH = 5 units. If the
perimeters of square OEFG and 3OGH are the same, find
(a) the value of x,
(b) the coordinates of E, F and H.
29. Find the area of quadrilateral ABCD in the figure.
C
A
B
y
x
0
5
-5 5
-5
y
x
O
E
H
F G
y
x
5
0
5
10
15
10 15
-5
-5
- 10
A
D
C
B
3
2
2
1
1
yes
5
(-4 , 1)
horizontal line
-2, 10
yes
3
325 sq. units
E(-3 , 0), F(-3 , -3), H(4 , -3)
R
Q
P