Q: 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\$.

(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)\$.

Q: 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.

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.

Q: 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?

\\( Given\quad that\quad ABCD\quad is\quad a\quad square\quad with\quad A\left( { x }_{ 1 },y_{ 1 } \right) =\left( 3,5 \right) ,\quad B\left( { x }_{ 2 },y_{ 2 } \right) =\left( 7,8 \right) \\ C\left( { x }_{ 3 },y_{ 3 } \right) =\left( 11,5 \right) \quad and\quad D\left( { x }_{ 4 },y_{ 4 } \right) =\left( 7,2 \right) .\\ \therefore \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 } \right) \quad or\quad M(x,y)=\left( \frac { { x }_{ 2 }+{ x }_{ 4 } }{ 2 } ,\frac { { y }_{ 2 }+{ y }_{ 4 } }{ 2 } \right) .\\ \Longrightarrow M(x,y)=\left( \frac { 3+11 }{ 2 } ,\frac { 5+5 }{ 2 } \right) \quad or\quad M(x,y)=\left( \frac { 7+7 }{ 2 } ,\frac { 8+2 }{ 2 } \right) \\ \Longrightarrow M(x,y)=\left( 7,5 \right) .\\ 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).\\ \\)

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

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.

Q: Which point lies on \$y\$-axis?

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.

Q: Ordinate of all points on the \$x\$-axis is:

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 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

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 3

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 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

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

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 $P$.&#10;&#10;Given,&#10;the point lies on $x$-axis.&#10;&#10;Then, its ordinate is $0$ or $y = 0$.&#10;&#10;Also, given the point is at a distance of $3$ units to the left of the origin.&#10;&#10;So, its abscissa will be $-3$.&#10;Hence, the co-ordinates of the required point are $(-3,0)$. &#10;&#10;Therefore, option $A$ is&#10;correct.

Question 7

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 8

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 9

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 10

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

Accepted Answer

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