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(Street Plan): A city has two main roads which cross each other at the centre of the city.
These two roads are along the North-South direction and East-West direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross-street is referred to in the following manner: If the 2nd street running in the North-South direction and 5 th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
(i) how many cross-streets can be referred to as (4, 3)?
(ii) how many cross-streets can be referred to as (3, 4)?
Write the answer of each of the following questions:
(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.
(i) The x-axis and the y-axis.
(ii) Quadrants.
(iii) The origin.
See figure and write the following:
(i) The coordinates of B.
(ii) The coordinates of C.
(iii) The point identified by the coordinates (-3, -5).
(iv) The point identified by the coordinates (2, - 4).
(v) The abscissa of the point D.
(vi) The ordinate of the point H.
(vii) The coordinates of the point L.
(viii) The coordinates of the point M.
(i) B → (- 5, 2)
(ii) C → (5, - 5)
(iii) E
(iv) G
(v) 6
(vi) - 3
(vii) L → (0, 5)
(viii) M → (- 3, 0)
(i) Coordinates of point A
(ii) Abscissa of point D
(iii) The point identified by the co-ordinates (5, 4)
(iv) Co-ordinates of point C
(i) A → (-7, 3)
(ii) D → (4, 5) (iii) B
(iv) (-3, -2)
In right triangle AOB OA2 + OB2 = AB2
| By Pythagoras Theorem
⇒ 42 + OB2 = 52
⇒ 16 + OB2 = 25
⇒ OB2 = 9
⇒ OB = 3
⇒ B → (0, 3)
The perpendicular distance of a point from the x-axis is 2 units and the perpendicular distance from the y-axis is 3 units. Write the coordinates of the point if it lies in the:
(i) I quadrant (ii) II quadrant
(iii) III quadrant (iv) IV quadrant
(i) (3, 2)
(ii) (-3, 2)
(iii) (-3, -2)
(iv) (3, -2)
∵ ∆ABC is an equilateral triangle
∴AC = BC = AB
⇒ BC = AB
⇒ BC = 2a
In right triangle COB,
OB2 + OC2 = BC2 
a2 + OC2 = (2a)2
OC2 + 3a2
Similarly, 
A → (-1, 3)
D → (2, -2)
Let D be the middle point of BC. Join AD. Then, ∠BDA = 90°
∵ ∆ABC is an equilateral triangle
∴AB = AC = BC
⇒ AB = BC
⇒ AB = 5 - 1 = 4 = BC BD = 3 - 1 = 2
In right triangle BDA,
AB2 = AD2 + BD2 
(4)2 = AD2 + (2)2
16 = AD2 + 4
AD2 = 12
AD = 
∵ ∆PQR is an equilateral triangle
∴ PQ = PR = QR
⇒ PQ = QR
⇒ PQ = 4
OQ = 2
In right triangle POQ,
OP2 + OQ2 = PQ2 |By Pythagoras Theorem
⇒ OP2 + (2)2 = (4)2
P → (3, 0)
Q → (0, -4)
R → (-5, 4)
S → (2, -3)
Find the co-ordinates of a point:
(i) whose ordinate is 6 and lies on y-axis.
(ii) whose abscissa is -3 and lies on x-axis.
(i)(0, 6)
(ii) (-3, 0)
In which quadrant, can a point have:
(i) abscissa equal to its ordinate
(ii) ordinate equal in magnitude to abscissa
(iii) ordinate equal and opposite of abscissa
(iv) abscissa twice that of the ordinate.
(i) I, III
(ii) I, II, III, IV
(iii) II, IV
(iv) I, III
(i) The abscissa and the ordinate of the point B are _ _ _ and _ _ _, respectively. Hence the coordinates of B are (_ _, _ _).
(ii) The x-coordinate and the y-coordinate of the point M are _ _ _ and _ _ _, respectively. Hence the coordinates of M are (_ _ _, _ _ _).
(iii) The x-coordinate and the y-coordinate of the point L are _ _ _ and _ _ _, respectively. Hence the coordinates of L are (_ _, _ _).
(iv) The x-coordinate and the y-coordinate of the point S are _ _ _ and _ _ _, respectively. Hence the coordinates of S are (_ _, _ _).
Solution not provided.
(i) 4, 3 (4, 3)
(ii) -3, 4, (-3, 4)
(iii) -5, -4, (- 5, -4)
(iv) 3, -4, (3, - 4)
Sponsor Area
Solution not provided.
Ans. 
In which quadrant do the given points lie?
(a) (2, -1) (b) (-1, 7)
(c) (-2, -3) (d) (4, 5)
Solution not provided.
Ans. (a) IV (b) II (c) III (d) I
Solution not provided.
Ans. 
(a) co-ordinates of B
(b) point identified by the coordinates (-2, -3)
(c) abscissa of point D (d) ordinate of point H
(e) points with the same abscissa
(f) points with the same ordinate
Solution not provided.
Ans. (a) (2, 3); (b) A; (c) 0; (d) 0; (e) M, D, H; B, G; (f) M, H
Solution not provided.
Ans. 
In which quadrant do the following points lie?
(a) (-4, -5) (b) (-3, 5)
(c) (2, 2) (d) (4, -1)
Solution not provided.
Ans. (a) III (b) II (c) IV
Find the co-ordinates of the point which lies on y-axis at a distance of 4 units in negative direction of y-axis.
(a) (-4, 0) (b) (4, 0)
(c) (0, -4) (d) (0,4)
Solution not provided.
Ans. C (0, -4)
Solution not provided.
Ans. 6 Units
Solution not provided.
Ans. (2, 3) (2, 0), (0, 3)
Observe the points plotted in the figure and find the following:
(i) The co-ordinates of E
(ii) The point with the co-ordinates (-4, -1)
(iii) The abscissa of A - abscissa of B
(iv) The ordinate of C + ordinate of F
Solution not provided.
Ans. (i) (-1, 2); (ii) D; (iii) - 2; (iv) 4
From given figure write the following:
(a) The coordinates of P
(b) The abscissa of the point Q
(c) The ordinate of the point R
(d) The points whose abscissa is O.
Solution not provided.
Ans. (a) (-3, -2); (b) 0, (c) 0, (d) R, Q, S, T
The perpendicular distance of a point from the x-axis is 4 units and the perpendicular distance from the y-axis is 5 units. Write the co-ordinates of such a point if it lies in the:
(i) I quadrant (ii) II quadrant
(iii) III quadrant (iv) IV quadrant
Solution not provided.
Ans. (i) (5, 4); (ii) (-5, 4); (iii) (-5, -4); (iv) (5, -4)
The perpendicular distance of a point from the x-axis is 2 units and the perpendicular distance from the y-axis is 5 units. Write the co-ordinates of such a point if it lies in the:
(i) I quadrant (ii) II quadrant
(iii) III quadrant (iv) IV quadrant
Solution not provided.
Ans. (i) (5, 2); (ii) (-5, 2); (iii) (-5, -2); (iv) (5, -2)
Find the co-ordinates of the points A, B, C, D, E and F. Which of the points are mirror images in
(i) x-axis (ii) y-axis
Solution not provided.
Ans.
The point (-2, 4) lies in the II quadrant.
The point (3, -1) lies in the IV quadrant.
The point (-1, 0) lies on the negative x-axis.
The point (1, 2) lies in the I quadrant.
The point (-3, -5) lies in the III quadrant.
The figure formed is a square.
Its all the sides are of equal length.
A → (-3, 0)
B → (3, 0)
C (3, 3)
D → (-3, 3)
Sponsor Area
The figure obtained is a rectangle.
Area of the rectangle = 4 × 6 = 24 square units
Example 8. Mark the points (2, 2), (2, -2), (-2, -2) and (-2, 2) on a graph paper and join these points. Name the figure that you obtain. Also, find the area of the figure so obtained.
Which of the following points lie on x-axis? Which on y-axis?
A (0, 2), B (5, 6), C (-3, 0), D (0, -3), E (0, 4), F (6, 0), G (3, 0)
The points C, F and G lie on x-axis.
The points A, D and E lie on y-axis.
Solution not provided.
Ans. 32 square units.
Solution not provided.
Ans. Straight line
Solution not provided.
Ans. Rectangle
Solution not provided.
Ans. Square; 4 Square units; 8 units
What are the co-ordinates of a point that is:
(i) the mirror image of point (0, 4) in x-axis
(ii) mirror image of point (-3, -5) in y-axis.
Solution not provided.
Ans. (i) (0, -4) (ii) (3, -5)
Sponsor Area
C.
at 0Tips: -
D.
IV and III quadrants respectivelyB.
I and IV quadrantsC.
Meeting place of two wallsC.
straight lineThe perpendicular distance of a point from the x-axis is 4 units and the perpendicular distance from the v-axis is 5 units. Write the coordinates of such a point if it lies in the
(a) I quadrant (b) II quadrant
(c) III quadrant (d) IV quadrant
Solution not provided.
Ans. (a) (5, 4) (b) (-5, 4) (c) (-5, -4) (d) (5, - 4)
Solution not provided.
Ans. Parallelogram: yes
In which quadrant do the following points lie?
(a) (-6, 2) (b) (-5, -4)
(c)(3, -2) (d) (9, 6)
Solution not provided.
Ans. (a) II (b) III (c) IV (d) I
Solution not provided.
Ans. (0, 0), (-p, 0), (-p, -q), (0, -q)
Locate and write the co-ordinates of a point:
(a) above x-axis lying on y-axis at a distance of 5 units from origin
(b) below x-axis lying on y-axis at a distance of 3 units from origin.
(c) lying on x-axis to the right of origin at a distance of 5 units.
(d) lying on x-axis to the left of origin at a distance of 2 units.
Solution not provided.
Ans. (a) (0, 5) (b) (0, -3) (c) (5, 0) (d) (-2, 0)
If the co-ordinates of a point M are (2, 9) which can also be expressed as (1 + x, y2) and y > 0, then find in which quadrant do the following points lie:
P (y, x), Q (2, x), R (x2, y - 1), S (2x, - 3y)
Solution not provided.
Ans.
P → I
Q → I
R → I
S → IV
Solution not provided.
Ans. A → (3, 4)
Plot the following points, join them and identify the figure thus obtained:
P (-1, 0), Q (2, 0), R (2, 3) and S (-1, 5).
Solution not provided.
Ans. Trapezium
In which quadrant or on which axes the following points lie?
P (-2, 4), Q (3, -1), R (-1, 0) and S (0, -4).
Solution not provided.
Ans. (P) II (Q)IV (R) x-axis (S) y-axis
Solution not provided.
Ans. C → (-2, -4)
Sponsor Area
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