Coordinate Geometry Test

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Coordinate Geometry Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

Abscissa of a point is positive in

A
$$I \, and \, II$$ quadrants

B
$$I \, and \, IV$$ quadrants

C
$$I$$ quadrant only

D
$$II$$ quadrant only

Solution

$$\textbf{Step -1: Observing the X-Y graph.}$$
$$\text{We can divide the X-Y graph into 4 quadrants where }$$
$$\text{x- +ve and y-+ve}\implies \text{1st quadrant}$$
$$\text{x- -ve and y- +ve}\implies \text{2nd quadrant}$$
$$\text{x- -ve and y- -ve}\implies \text{3rd quadrant}$$
$$\text{x-+ve and y- - ve}\implies \text{4th quadrant}$$
$$\textbf{Step -2: Finding points with positive abscissa}$$
$$\text{On observing the graph we can see that the x-coordinate of a point is positive in the }I $$
$$\text{ and }IV \text{ quadrants}$$
$$\textbf{Hence, the abscissa of a point is positive in the }\mathbf{I \text{ and } IV \text{ quadrants .} }$$
Question 2
1 / -0

If y - coordinate of a point is zero, then this point always lies

A
in $$I$$ quadrant

B
in $$II$$ quadrant

C
on x- axis

D
on y - axis

Solution

We know that if y - coordinate of a point, i.e ...., ordinate is zero, then this point always lies on x - axis.
Hence, $$\left(C\right)$$ is the correct answer.
Question 3
1 / -0

If $$P \left(-1,1\right), Q \left(3,-4\right), R \left(1,-1\right), S \left(-2,-3\right)$$ and $$T \left(-4,4\right)$$ are plotted on the graph paper, then the points in the fourth quadrant are:

A
P and T

B
Q and R

C
Only S

D
P and R

Solution

We know that quadrant $$IV$$ consists of all the points $$\left(x,y\right)$$ for which x is positive and y negative, So, the points in the fourth quadrants are $$Q \left(3,-4\right) \, and \, R \left(1, -1\right)$$.
Hence, $$\left(B\right)$$ is the correct answer.
Question 4
1 / -0

Point $$\left(0, -7\right)$$ lies

A
On the x -axis

B
in the second quadrant

C
on the y-axis

D
in the forth quadrant

Solution

In Point $$\left(0,-7\right)$$ co-ordinate of x - axis is zero so it lies on y - axis.
Hence, $$\left( C\right)$$ is the correct answer.
Question 5
1 / -0

Point $$\left(-3,5\right)$$ lies in the

A
First quadrant

B
Second quadrant

C
Third quadrant

D
Fourth quadrant

Solution

Every point on second quadrant has value of abscissa negative and its ordinate is positive.
Point $$\left(-3,5\right)$$ has abscissa is negative and ordinate is positive. So, it lies in the second quadrant.
Hence, $$\left(B\right)$$ second quadrant, is the correct answer.
Question 6
1 / -0

If $$P \left(5, 1 \right), Q \left(8,0\right), R \left(0,4\right), S \left(0,5\right)$$ and $$ O \left(0,0 \right)$$ are plotted on the graph paper, then the point $$\left(s\right)$$ on the x - axis are

A
P and R

B
R and S

C
Only Q

D
Q and O

Solution

We now that, a point lies on X - axis, if its y - coordinate is zero.
So, the points on the axis are Q(8,0) is the correct answer.
Question 7
1 / -0

Which of the points $$P \left(0,3\right), Q \left(1,0\right),R \left(0,-1\right),S \left(-5,0\right),T \left(1,2\right)$$ 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

We know that a point on the a-axis has always its ordinate equal to $$0$$. So, the points which do not lies the x - axis are $$P \left(0,3\right),R \left(0,-1\right) \, and\, T \left(1,2\right)$$.
Hence, $$\left(C\right)$$ is the correct answer.
Question 8
1 / -0

The point whose ordinate is $$4$$ and which lies on y - axis is

A
$$\left(4,0\right)$$

B
$$\left(0,4\right)$$

C
$$\left(1,4\right)$$

D
$$\left(4,2\right)$$

Solution

$${\textbf{Step  -  1 : Apply properties of y axis}}{\text{.}}$$
$${\text{We know that any point, suppose }}\left( {{x,y}} \right){\text{ on Y axis will have }x = 0}{\text{. }}$$
$${\text{hence, any point on Y axis will be in the form of }}\left( {0,{y}} \right).$$
$${\textbf{Step  -  2 : Determine the point}}{\text{.}}$$
$${\text{So given that the  ordinate is 4}}{\text{.}}$$
  $${\text{To be on Y axis it must be of form }}\left( {0,{y}} \right).$$
  $${\text{So simply the point will be }}\left( {0,4} \right)$$
$${\textbf{Hence, the point with ordinate 4 and on Y axis is }} \mathbf{ \left({0,4} \right).}$$
Question 9
1 / -0

The point which lies on y - axis at a distance of $$5$$ units in the negative direction of y - axis is:

A
$$ \left(0,5\right)$$

B
$$ \left(5,0\right)$$

C
$$ \left(0,-5\right)$$

D
$$ \left(-5,0\right)$$

Solution

Given the point lies on Y-axis this shows that its x - coordinate is zero. Also, it is at a distance of $$5$$ units in the negative direction of Y - axis, so its y - coordinate is negative. Hence, the required point is $$\left(0,-5\right)$$.
Hence, $$\left(A\right)$$ is the correct answer.
Question 10
1 / -0

Abscissa of a point is positive in

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

B
$$I$$ and $$IV$$ quadrants

C
$$I$$ quadrant only

D
$$II$$ quadrant only

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.
The signs of the coordinates in the first quadrant is $$(+,+)$$,
the second quadrant is $$(-,+)$$,
the third quadrant is $$(-,-)$$,
fourth quadrant is $$(+,-)$$.
So, the abscissa of the point is positive in the first and fourth quadrant.

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Coordinate Geometry Test - 28

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Coordinate Geometry Test - 28

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Question 1

$$I \, and \, II$$ quadrants

$$I \, and \, IV$$ quadrants

$$I$$ quadrant only

$$II$$ quadrant only

Solution

Question 2

in $$I$$ quadrant

in $$II$$ quadrant

on x- axis

on y - axis

Solution

Question 3

P and T

Q and R

Only S

P and R

Solution

Question 4

On the x -axis

in the second quadrant

on the y-axis

in the forth quadrant

Solution

Question 5

First quadrant

Second quadrant

Third quadrant

Fourth quadrant

Solution

Question 6

P and R

R and S

Only Q

Q and O

Solution

Question 7

P and R only

Q and S only

P,R and T

Q,S and T

Solution

Question 8

$$\left(4,0\right)$$

$$\left(0,4\right)$$

$$\left(1,4\right)$$

$$\left(4,2\right)$$

Solution

Question 9

$$ \left(0,5\right)$$

$$ \left(5,0\right)$$

$$ \left(0,-5\right)$$

$$ \left(-5,0\right)$$

Solution

Question 10

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

$$I$$ and $$IV$$ quadrants

$$I$$ quadrant only

$$II$$ quadrant only

Solution

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