EXERCISE 5
Question 1:
On the plane of a graph paper draw X'OX and YOY' as coordinate axes and plot each of the following points.
(i) A(5, 3)
(ii) B(6, 2)
(iii) C(–5, 3)
(iv) D(4, –6)
(v) E(–3, –2)
(vi) F(–4, 4)
(vii) G(3, –4)
(viii) H(5, 0)
(ix) I(0, 6)
(x) J(–3, 0)
(xi) K(0, –2)
(xii) O(0, 0)
Answer 1:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
(xi)
(xii)
Question 2:
Write down the coordinates of each of the points A, B, C, D, E shown below:
Answer 2:
Draw perpendicular AL, BM, CN, DP and EQ on the X-axis.
(i) Distance of A from the Y-axis = OL = -6 units
Distance of A from the X-axis = AL = 5 units
Hence, the coordinates of A are (-6,5).
(ii) Distance of B from the Y-axis = OM = 5 units
Distance of B from the X-axis = BM = 4 units
Hence, the coordinates of B are (5,4).
(iii) Distance of C from the Y-axis = ON = -3 units
Distance of C from the X-axis = CN = 2 units
Hence, the coordinates of C are (-3,2).
(iv) Distance of D from the Y-axis = OP = 2 units
Distance of D from the X-axis = DP = -2 units
Hence, the coordinates of D are (2,-2).
(v) Distance of E from the Y-axis = OL = -1 units
Distance of E from the X-axis = AL = -4 units
Hence, the coordinates of E are (-1,-4).
Question 3:
For each of the following points, write the quadrant in which it lies
(i) (–6, 3)
(ii) (–5, –3)
(iii) (11, 6)
(iv) (1, –4)
(v) (–7, –4)
(vi) (4, –1)
(vii) (–3, 8)
(viii) (3, –8)
Answer 3:
(i) (–6, 3)
Points of the type (–, +) lie in the II quadrant.
Hence, the point lies (–6, 3) in the II quadrant.
(ii) (–5, –3)
Points of the type (–, –) lie in the III quadrant.
Hence, the point lies (–5, –3) in the III quadrant.
(iii) (11, 6)
Points of the type (+, +) lie in the I quadrant.
Hence, the point lies (11, 6) in the I quadrant.
(iv) (1, –4)
Points of the type (+, –) lie in the IV quadrant.
Hence, the point lies (1, –4) in the IV quadrant.
(v) (–7, –4)
Points of the type (–, –) lie in the III quadrant.
Hence, the point lies (–7, –4) in the III quadrant.
(vi) (4, –1)
Points of the type (+, –) lie in the IV quadrant.
Hence, the point lies (4, –1) in the IV quadrant.
(vii) (–3, 8)
Points of the type (–, +) lie in the II quadrant.
Hence, the point lies (–3, 8) in the II quadrant.
(viii) (3, –8)
Points of the type (+, –) lie in the IV quadrant.
Hence, the point lies (3, –8) in the IV quadrant.
Question 4:
Write the axis on which the given point lies.
(i) (2, 0)
(ii) (0, –5)
(iii) (–4, 0)
(iv) (0, –1)
Answer 4:
(i) (2, 0)
The ordinate of the point (2, 0) is zero.
Hence, the (2, 0) lies on the x-axis.
(ii) (0, –5)
The abscissa of the point (0, –5) is zero.
Hence, the (0, –5) lies on the y-axis.
(iii) (–4, 0)
The ordinate of the point (–4, 0) is zero.
Hence, the (–4, 0) lies on the x-axis.
(iv) (0, –1)
The abscissa of the point (0, –1) is zero.
Hence, the (0, –1) lies on the y-axis.
Question 5:
Which of the following points lie on the x-axis?
(i) A(0, 8)
(ii) B(4, 0)
(iii) C(0, –3)
(iv) D(–6, 0)
(v) E(2, 1)
(vi) F(–2, –1)
(vii) G(–1, 0)
(viii) H(0, –2)
Answer 5:
(i) A(0, 8)
The given point does not lies on the x-axis.
(ii) B(4, 0)
The ordinate of the point (4, 0) is zero.
Hence, the (4, 0) lies on the x-axis.
(iii) C(0, –3)
The given point does not lies on the x-axis.
(iv) D(–6, 0)
The ordinate of the point (–6, 0) is zero.
Hence, the (–6, 0) lies on the x-axis.
(v) E(2, 1)
The given point does not lies on the x-axis.
(vi) F(–2, –1)
The given point does not lies on the x-axis.
(vii) G(–1, 0)
The ordinate of the point (–1, 0) is zero.
Hence, the (–1, 0) lies on the x-axis.
(viii) H(0, –2)
The given point does not lies on the x-axis.
Question 6:
Plot the points A(2, 5), B(–2, 2) and C(4, 2) on a graph paper. Join AB, BC and AC. Calculate the area of ∆ABC.
Answer 6:
Abscissa of D = Abscissa of A = 2
Ordinate of D = Ordinate of B = 2
Now,
BC = (2 + 4) units = 6 units
AD = (5 – 2) units = 3 units
Hence, area of ∆ABC is 9 square units.
Question 7:
Three vertices of a rectangle ABCD are A(3, 1), B(–3, 1) and C(–3, 3). Plot these points on a graph paper and find the coordinates of the fourth vertex D. Also, find the area of rectangle ABCD.
Answer 7:
Let A(3, 1), B(–3, 1) and C(–3, 3) be three vertices of a rectangle ABCD.
Let the y-axis cut the rectangle ABCD at the points P and Q respectively.
Abscissa of D = Abscissa of A = 3.
Ordinate of D = Ordinate of C = 3.
∴ coordinates of D are (3, 3).
AB = (BP + PA) = (3 + 3) units = 6 units.
BC = (OQ – OP) = (3 – 1) units = 2 units.
Ar(rectangle ABCD) = (AB × BC)
= (6 × 2) sq. units
= 12 sq. units
Hence, the area of rectangle ABCD is 12 square units.
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