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: 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.

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.

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

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

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

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

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 10

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

Accepted Answer

The point at which the coordinate axes meet is called the origin. The point is denoted by $O$ in the above image.