Question 1

Plot the following points on a graph paper and find out in which quadrant do they lie? (i) A (3,5)  (ii) B (-2 , 7) (iii) C (-3,-5)    (iv) D (2, -7) (v) O (0, 0)

Accepted Answer

Draw the x and y axes. Mark the units along the x and y axes with a suitable scale.(i) To plot the point A (3 , 5)       Here, the x-coordinate of A is 3 and the y-coordinate of A is 5. Both are positive. Hence the point A (3 , 5) lies in the  quadrant I. Start at the Origin. Move three units to the right along the x-axis. Then turn and move 5 units up parallel to Y-axis and mark the point A (3 , 5). (ii) To plot the point B (2 , 7)      Here, the x-coordinate of B is -2 which is negative and the y-coordinate of B is 7 which is positive. Hence the point  B (-2 , 7) lies in the quadrant II. Start at the Origin. Move 2 units to the left along the x-axis. Then  turn and move 7 units up parallel to y-axis and mark the point B (-2 , 7). (iii) To plot the point C (-3 , -5) Here, the x-coordinate of C is -3 and the y-coordinate of C is -5. Both are negative. Hence the point C (-3 , -5) lies in the quadrant III. Start at the Origin. Move 3 units to the left along the x-axis. Then turn and move 5 units down parallel to y-axis. and mark the point C (-3, -5). (iv) To plot the point D (2 , 7)       Here, the  x-coordinate of the point D is 2 which is positive and the y-coordinate of D is -7 which is negative. Hence the point D (2 , -7) lies in the quadrant IV. Start at the Origin. Move 2 units to the right along the x-axis. Then turn and move 7 units down parallel to y-axis and mark the point D (2 , -7). (v) To plot the point O (0, 0)       This is the origin. Both the x and y coordinates are zeros. It is the point of  intersection of the axes x and y. Mark the point O (0,0).

Question 2

See the 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 .

Accepted Answer

(i) The coordinate of  B  is  (-5, 2) .(ii) The coordinate of  C  is  (5, -5) .(iii) The point identified by the coordinate  (-3, -5)  is  E .(iv) The point identified by the coordinate  (2, -4)  is  G .(v) Abscissa means  x  coordinate of the point  D . So, the abscissa of the point  D  is  6 .(vi) Ordinate means  y  coordinate of point  H . So, ordinate of point  H  is  -3 .(vii) The coordinates of the point  L  is  (0, 5) .(viii) The coordinates of the point  M  is  (- 3, 0) .

Question 3

Plot the following points on a graph paper and find out where do they lie? (i) A (7, 0) (ii) B (-5, 0) (iii) C (0 , 4) (iv) D (0, -3)

Accepted Answer

Draw the x and y axes. Mark the units along the x and y axes with a suitable scale. (i) To plot the point A (7, 0)       Here, the  x-coordinate of A is 7 which is positive and the y-coordinate of  A is zero. Hence the point A (7, 0) lies on the x-axis. Start at the Origin. Move 7 units to the right along the x-axis and mark it. (ii) To plot the point B (-5 , 0)         Here, the x-coordinate of B is 5 which is negative and the y-coordinate is zero. Hence the point B (-5 , 0) lies on the x-axis. Start at the Origin. Move 5 units to the left along the x-axis and mark it. (iii) To lot the point C (0 ,4)       Here, the x-coordinate of C is zero and the y-coordinate of C is 4 which is positive. Hence the point  C (0 , 4) lies on the y-axis. Start at the Origin. Move 4 units up along the y-axis and mark it. (iv) To plot the point D (0 , -3)       Here the x-coordinate of D is zero and the  y-coordinate of D is -3 which is negative. Hence the point D (0 , -3) lies on the y-axis. Start at the Origin. Move 3 units down along the y-axis and mark it.

Question 4

In which quadrant or on which axis do each of the points  (-2, 4), (3, -1), (-1, 0), (1, 2)  and  (-3, -5)  lie? Verify your answer by locating them on the Cartessian plane.

Accepted Answer

Point  (1,2)  lies in the  1^{st}  quadrant.Point  (-2,4)  lies in the  2^{nd}  quadrant.Point  (-3,-5)  lies in the  3^{rd}  quadrant.Point  (3,-1)  lies in the  4^{th}  quadrant.Point  (-1,0)  lies on the negative side of  x -axis.

Question 5

Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure 7.4. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?

Accepted Answer

Given\quad that\quad ABCD\quad is\quad a\quad square\quad with\quad A\left( { x }_{ 1 },y_{ 1 } ight) =\left( 3,5 ight) ,\quad B\left( { x }_{ 2 },y_{ 2 } ight) =\left( 7,8 ight) \ C\left( { x }_{ 3 },y_{ 3 } ight) =\left( 11,5 ight) \quad and\quad D\left( { x }_{ 4 },y_{ 4 } ight) =\left( 7,2 ight) .\ 	herefore \quad The\quad position\quad of\quad Jaspal\quad will\quad be\quad the\quad mid\quad point\quad M(x,y)\ between\quad AC\quad or\quad BD.\quad (AC=BD\quad \because \quad ABCD\quad is\quad a\quad square).\ By\quad the\quad section\quad formula\quad for\quad the\quad mid\quad point\quad \ M(x,y)=\left( \frac { { x }_{ 1 }+{ x }_{ 3 } }{ 2 } ,\frac { { y }_{ 1 }+{ y }_{ 3 } }{ 2 }  ight) \quad or\quad M(x,y)=\left( \frac { { x }_{ 2 }+{ x }_{ 4 } }{ 2 } ,\frac { { y }_{ 2 }+{ y }_{ 4 } }{ 2 }  ight) .\ \Longrightarrow M(x,y)=\left( \frac { 3+11 }{ 2 } ,\frac { 5+5 }{ 2 }  ight) \quad or\quad M(x,y)=\left( \frac { 7+7 }{ 2 } ,\frac { 8+2 }{ 2 }  ight) \ \Longrightarrow M(x,y)=\left( 7,5 ight) .\ So\quad the\quad position(co-ordinates)\quad of\quad Jaspal\quad is\quad (7,5).\ Ans-\quad The\quad position(co-ordinates)\quad of\quad Jaspal\quad is\quad (7,5).\

Question 6

The coordinates of a point, lies on  x -axis and is at a distance of  3  units to the left of the origin is _____.

Accepted Answer

Let the required point be  P .

Given,
the point lies on  x -axis.

Then, its ordinate is  0  or  y = 0 .

Also, given the point is at a distance of  3  units to the left of the origin.

So, its abscissa will be  -3 .
Hence, the co-ordinates of the required point are  (-3,0) .

Therefore, option  A  is
correct.

Question 7

Which point lies on  y -axis?

Accepted Answer

We know, any point which lies on the  y -axis will be of the form  (0,y) , where  y  is any real number.Here, the points  (0,4)  and  (0,-8)  are of the form  (0,y) , where  y=4  and  -8 , respectively.Therefore, options  B  and  D  is correct.

Question 8

Ordinate of all points on the  x -axis is:

Accepted Answer

We know, the coordinates of  x -axis is  (x,0) .Then,  the coordinates of any point on the  x -axis is  (x,0) ,where the abscissa is  x  and the ordinate is  0 . Therefore, the ordinate of any point on the  x -axis is  0 .Hence, option  A  is correct.

Question 9

On which axis do the following points lie?(i)  P(5,0)   (ii)  Q(0.-2)   (iii)  R(-4,0)   (iv)  S(0,5)

Accepted Answer

If the point lies on the x-axis, y co-ordinate =0If the point lies on the y-axis, x co-ordinate =0 P(5,0)    y co-ordinate=0, so the point lies on x-axis Q(0,-2)  x co-ordinate=0, so the point lies on y-axis R(-4,0)   y co-ordinate=0, so the point lies on x-axis S(0,5)    x co-ordinate=0, so the point lies on y-axis

Question 10

The point at which the two coordinate axes meet is called the

Accepted Answer

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