Coordinate Geometry Test

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Coordinate Geometry Test - 29

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Question 1
1 / -0

The points whose abscissa and ordinate have different signs will lie in:

A
$$I$$ and $$II$$ quadrants

B
$$II$$ and $$III$$ quadrants

C
$$I$$ and $$III$$ quadrants

D
$$II$$ and $$IV$$ quadrants

Solution

A coordinate is an ordered pair of numbers in which the first number is the abscissa i.e. the measurement along the $$X$$ axis and the second number is the ordinate i.e, the measurement along the $$Y$$ axis.

The signs of the coordinates in the first quadrant is $$(+,+)$$,
the second quadrant is $$(-,+)$$,
the third quadrant is $$(-,-)$$,
fourth quadrant is $$(+,-)$$.
So, the points whose abscissa and ordinate have different signs are $$2^{nd}$$ and $$4^{th}$$ quadrants.
Question 2
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The point $$(0, 7)$$ lies:

A
On the $$x$$-axis

B
In the second quadrant

C
On the $$y$$-axis

D
In the fourth quadrant

Solution

The coordinates of the given point is $$(0,7)$$, i.e. the abscissa is $$0$$.
We know, the coordinates of a point in the form $$(0,y)$$ lies in the $$y$$-axis.
$$\therefore (0,7)$$ lies on the $$y$$-axis.
Here, the ordinate is $$7$$, and is positive.
$$\therefore $$ $$(0,7)$$ lies on the positive side of the $$y$$-axis.

Therefore, option $$C$$ is correct.
Question 3
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The point $$(3, 5)$$ lies in which quadrant in the Cartesian coordinate plane?

A
first quadrant

B
second quadrant

C
third quadrant

D
fourth quadrant

Solution

Since, the $$x$$-coordinate and the $$y$$-coordinate are both positive, the point $$(3,5)$$ lies in the first quadrant of the Cartesian plane.

Therefore, option $$A$$ is correct.
Question 4
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Signs of the abscissa and ordinate of a point in the second quadrant are respectively:

A
$$+, +$$

B
$$-,-$$

C
$$- , +$$

D
$$+,-$$

Solution

The signs of the $$x$$ and $$y$$ co-ordinates in the $$4$$ quadrants are as tabulated below:

Quadrant $$x$$ $$y$$
$$\text{I}$$ $$+$$ $$+$$
$$\text{II}$$ $$-$$ $$+$$
$$\text{III}$$ $$-$$ $$-$$
$$\text{IV}$$ $$+$$ $$-$$
From the table, it can be observed that in the second quadrant, $$x$$ is negative and $$y$$ is positive hence the coordinates of a point in the second quadrant will have sign of the form $$(-, +)$$.
Question 5
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Which of the points $$P(0, 3), Q(1, 0), R(0, 1), S(5, 0), T(1, 2)$$ do not lie on the $$x$$-axis?

A
$$P$$ and $$R$$ only

B
$$Q$$ and $$S$$ only

C
$$P, R$$ and $$T$$

D
$$Q, S$$ and $$T$$

Solution

Any point which do not lie on the $$x-$$ axis has coordinates of the form $$(x,y)$$, where $$y\neq0$$
From the given points,
in $$P(0,3),$$ $$y=3\neq 0$$,
in $$Q(1,0),$$ $$y=0$$,
in $$R(0,1),$$ $$y=1\neq 0$$,
in $$S(5,0),$$ $$y=0$$
and in $$T(1,2),$$ $$y=2\neq 0$$.

We can see that, the coordinates of points $$P,R$$ and $$T$$ have $$y\neq 0$$.
Thus, $$P,R$$ and $$T$$ do not lie on the $$x-$$ axis.
Hence, option $$C$$ is correct.
Question 6
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If $$P (1, 1), Q (-3,- 4), R(-1,- 1), S(2, 3)$$ and $$T ( 4, 4)$$ are plotted on the graph paper, then the point(s) in the third quadrant are:

A
$$P$$ and $$T$$

B
$$Q$$ and $$R$$

C
Only $$S$$

D
$$P$$ and $$R$$

Solution

We know that in third quadrant both the coordinates i.e, $$x,y$$ are negative.
Now the given points are
$$P(1,1), Q(-3,-4), R(-1,-1), S(2,3) $$ and $$T(4,4)$$.
Among them, $$Q$$ and $$R$$ have both the coordinates negative.
$$\therefore$$ points $$Q$$ and $$R$$ are in third quadrant.
Question 7
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The diagram shows the four quadrants P, Q R and S on a Cartesian plane.
Which of the following points lie in quadrant S?
I (-1, 2)
II (-1, -2)
III (1, -2)
IV (2,-1)

A
I and II only

B
I and IV only

C
II and III only

D
III and IV only

Solution

The coordinates of any point on 2D plane is given in form of (x,y) coordinates where x-coordinate is the coordinates along X-plane and similarly y-coordinate along Y plane

In order to be a point in 4th Quadrant, the value of x has to be positive and the value of Y should be negative.

Hence the points III and IV are in the 4th Quadrant.
Question 8
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From the given figure, write the points whose abscissa is $$0$$.

A
$$I, O$$ and $$G$$

B
$$A, L$$ and $$O$$

C
$$A, I$$ and $$O$$

D
$$L, K ,O$$ and $$M$$

Solution

The abscissa of the points, which lie on the $$y$$-axis are $$0$$.
Here, from the given graph, the points $$A,O$$ and $$L$$ lies on $$y$$-axis and have coordinates $$A(0,3), L(0,-4)$$ and $$O(0,0)$$, and their abscissae are $$0$$.
Therefore, the points $$A,O$$ and $$L$$ lie on $$y$$-axis and have abscissa $$0$$.

Therefore, option $$B$$ is correct.
Question 9
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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?

A
$$(7, 5)$$

B
$$(5, 7)$$

C
$$(4, 6)$$

D
$$(6, 4)$$

Solution

$$ Given\quad that\quad ABCD\quad is\quad a\quad square\quad with\quad A\left( { x }_{ 1 },y_{ 1 } \right) =\left( 3,5 \right) ,\quad B\left( { x }_{ 2 },y_{ 2 } \right) =\left( 7,8 \right) \\ C\left( { x }_{ 3 },y_{ 3 } \right) =\left( 11,5 \right) \quad and\quad D\left( { x }_{ 4 },y_{ 4 } \right) =\left( 7,2 \right) .\\ \therefore \quad The\quad position\quad of\quad Jaspal\quad will\quad be\quad the\quad mid\quad point\quad M(x,y)\\ between\quad AC\quad or\quad BD.\quad (AC=BD\quad \because \quad ABCD\quad is\quad a\quad square).\\ By\quad the\quad section\quad formula\quad for\quad the\quad mid\quad point\quad \\ M(x,y)=\left( \frac { { x }_{ 1 }+{ x }_{ 3 } }{ 2 } ,\frac { { y }_{ 1 }+{ y }_{ 3 } }{ 2 } \right) \quad or\quad M(x,y)=\left( \frac { { x }_{ 2 }+{ x }_{ 4 } }{ 2 } ,\frac { { y }_{ 2 }+{ y }_{ 4 } }{ 2 } \right) .\\ \Longrightarrow M(x,y)=\left( \frac { 3+11 }{ 2 } ,\frac { 5+5 }{ 2 } \right) \quad or\quad M(x,y)=\left( \frac { 7+7 }{ 2 } ,\frac { 8+2 }{ 2 } \right) \\ \Longrightarrow M(x,y)=\left( 7,5 \right) .\\ So\quad the\quad position(co-ordinates)\quad of\quad Jaspal\quad is\quad (7,5).\\ Ans-\quad The\quad position(co-ordinates)\quad of\quad Jaspal\quad is\quad (7,5).\\ $$
Question 10
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From the figure, write the points whose ordinate is $$0$$.

A
$$G, I$$ and $$O$$

B
$$A, L$$ and $$O$$

C
$$A, I$$ and $$O$$

D
$$K, L, O$$ and $$M$$

Solution

The ordinate of the points, which lies on the $$x$$-axis are $$0$$.
Here, from the given graph, the points $$I,O$$ and $$G$$ lies on $$x$$-axis and have coordinates $$I(-2,0), G(5,0)$$ and $$O(0,0)$$, respectively and their ordinates are $$0$$.
Therefore, the points $$I,O$$ and $$G$$ lies on $$x$$-axis and have ordinate $$0$$.

Therefore, option $$A$$ is correct.