Coordinate Geometry Test

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Coordinate Geometry Test - 18

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Weekly Quiz Competition

Question 1
1 / -0

Any point on the $$x$$-axis is of the form:

A
$$(x, y)$$

B
$$(0, y)$$

C
$$(x, 0)$$

D
$$(x, x)$$

Solution

In the $$xy$$-plane, any point on the $$x$$-axis will have $$y =0$$.
Hence, any point on the $$x$$-axis is of the form $$(x,0)$$.

Therefore, option $$C$$ is correct.
Question 2
1 / -0

Without plotting the point indicate the quadrant in which the point will lie, if ordinate is $$5$$ and abscissa is $$3$$?

A
$$ I$$

B
$$ II$$

C
$$ III$$

D
$$ IV$$

Solution

Given ordinate or $$y$$-coordinate $$= 5$$
and abscissa or $$x$$-coordinate $$=3$$
$$\therefore$$ $$(x ,y)$$ = $$(3,5)$$
Since, both the coordinates are positive
The point will lie in $$Quadrant-I$$
Question 3
1 / -0

Which of the given points lie on $$y$$-axis?
$$A (1, 1), B (1, 0), C (0, 1), D (0, 0), E (0, 1), F ( 1, 0), G (0, 5), H ( 7, 0), I (3, 3)$$.

A
$$B, D, F, H$$

B
$$A, C, E, H$$

C
$$C, D, E, G$$

D
$$B, D, F, G$$

Solution

If a point is on $$y$$-axis , then the $$x$$ co-ordinate of that point should be zero.
Here, the $$x$$-coordinate is zero at:
$$C(0,1)$$,
$$D(0,0)$$,
$$E(0,1)$$
and $$G(0,5)$$.
Therefore, these points lies on the $$y$$-axis.

Hence, option $$C$$ is correct.
Question 4
1 / -0

Write the name of the quadrant in which the point $$( - 3, 5)$$ lies.

A
First quadrant

B
Second quadrant

C
Third quadrant

D
Fourth quadrant

Solution

The point $$(-3,5)$$ lies at second quadrant
Question 5
1 / -0

Without plotting the point, indicate the quadrant in which the given point will lies whose ordinate is $$-5$$ and abscissa is $$3$$?

A
$$ I$$

B
$$ II$$

C
$$ III$$

D
$$ IV$$

Solution

Given: The abscissa is $$+3$$ & ordinate is $$-5$$

We know that in $$ I^{st}$$ quadrant, both the abscissa and ordinate are positive.

In $$II^{nd}$$ quadrant, the abscissa is negative and the ordinate is positive.

In $$III^{rd}$$ quadrant, the abscissa is negative and the ordinate is negative.

In $$IV^{th}$$ quadrant, the abscissa is positive and the ordinate is negative.

$$\\ \therefore$$ The point lies in the $$IV^{th}$$ quadrant.
Question 6
1 / -0

In which quadrant the point $$(2,-3)$$ will lie?

A
First

B
Second

C
Third

D
Fourth

Solution

Given point is $$(2,-3)$$
Since $$x-$$coordinate is positive and $$y-$$coordinate is negative, the given point will lie in the fourth quadrant.

Hence, option D is correct.
Question 7
1 / -0

Without plotting the points indicate the quadrant in which the point will lie, if abscissa is $$-5$$ and ordinate is $$-3$$?

A
$$ I$$

B
$$ II$$

C
$$ III$$

D
$$ IV$$

Solution

In $$\text{I}$$ quadrant, abscissa and ordinates are positive.
In $$\text{II}$$ quadrant, abscissa is negative and ordinate is positive.
In $$\text{III}$$ quadrant, both abscissa and ordinate are negative.
In $$\text{IV}$$ quadrant, abscissa is positive and ordinate is negative.
Here, the given abscissa is $$-5$$ and ordinate is $$-3$$. Both are negative.
Thus, they lie in $$\text{III} $$ quadrant.
Hence, option $$C$$ is correct.
Question 8
1 / -0

Any point on the line $$y = x $$ is of the form

A
$$(a, a)$$

B
$$(0, a)$$

C
$$(a, 0)$$

D
$$(-a, a)$$

Solution

$${\textbf{Step - 1: Plot and identify points in the Cartesian plane.}}$$

$${\text{The given equation is}}$$ $$x = y.$$

$${\text{So, if}}$$ $$x = 1$$ $${\text{and}}$$ $$y = 1.$$

$${\text{If}}$$ $$x = -5$$ $${\text{and}}$$ $$y = -5.$$

$${\text{If}}$$ $$x = 0$$ $${\text{and}}$$ $$y = 0.$$
$${\textbf{Step - 2: By Induction.}}$$

$$x = a$$ $${\text{and}}$$ $$y = a.$$

$${\text{So, any point P on the line}}$$ $$x = y$$ $${\text{will be of the form}}$$ $$\text{P} (a, a).$$

$${\textbf{ Hence the correct option (A) (a, a).}}$$
Question 9
1 / -0

State whether True or False:
A point whose $$y$$-coordinate is zero and $$x$$-coordinate is $$5$$ will lie on the $$y$$-axis.

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

The given point has $$y$$-coordinate as zero and $$x$$-coordinate as $$5$$.
So, the point is $$(5,0)$$ and it lies on $$x$$-axis and not $$y$$-axis.
Thus, the given statement is false.
Therefore, option $$B$$ is correct.
Question 10
1 / -0

The points $$(- 5,2)$$ and $$(2, - 5)$$ lie in the :

A
same quadrants

B
II and III quadrants respectively

C
II and IV quadrants respectively

D
IV and III quadrants respectively

Solution

$$\therefore$$ The point $$(-5,2)$$ lies at quadrant $$II$$ and point $$(2,-5)$$ lies at quadrant $$IV$$

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Coordinate Geometry Test - 18

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Coordinate Geometry Test - 18

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Question 1

$$(x, y)$$

$$(0, y)$$

$$(x, 0)$$

$$(x, x)$$

Solution

Question 2

$$ I$$

$$ II$$

$$ III$$

$$ IV$$

Solution

Question 3

$$B, D, F, H$$

$$A, C, E, H$$

$$C, D, E, G$$

$$B, D, F, G$$

Solution

Question 4

First quadrant

Second quadrant

Third quadrant

Fourth quadrant

Solution

Question 5

$$ I$$

$$ II$$

$$ III$$

$$ IV$$

Solution

Question 6

First

Second

Third

Fourth

Solution

Question 7

$$ I$$

$$ II$$

$$ III$$

$$ IV$$

Solution

Question 8

$$(a, a)$$

$$(0, a)$$

$$(a, 0)$$

$$(-a, a)$$

Solution

Question 9

True

False

Ambiguous

Data insufficient

Solution

Question 10

same quadrants

II and III quadrants respectively

II and IV quadrants respectively

IV and III quadrants respectively

Solution

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