Coordinate Geometry Test

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Coordinate Geometry Test - 24

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Weekly Quiz Competition

Question 1
1 / -0

A point both of whose co-ordinates are negative will lie in _____ quadrant

A
$$I$$

B
$$II$$

C
$$III$$

D
$$IV$$

Solution

$$XY$$ plane is divided into four quadrants.
$$1^{st}$$ quadrant has both coordinates positive, $$2^{nd}$$ quadrant has $$x$$ negative and $$y$$ positive.
$$3^{rd}$$ quadrant has both the coordinates negative.

Hence, the answer is $$3^{rd}$$ quadrant.
Question 2
1 / -0

Abscissa of a point is positive in _____ quadrant

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

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

C
$$III$$ and $$IV$$

D
$$IV$$ and $$I$$

Solution

Abscissa of a point means the $$x$$ co-ordinate of the point.
Points that lie in the $$I$$ and $$IV$$ quadrants have their $$x$$ co-ordinates positive.
So, option $$D$$ is correct,
Question 3
1 / -0

What is the ordinate of point $$D$$?

A
$$-6$$

B
$$4$$

C
$$-2$$

D
$$10$$

Solution

The required point is $$D$$.
Here, the point is at a distance of $$6$$ units left of the $$y$$-axis $$\implies x=-6$$.
Also, the point is at a distance of $$4$$ units above the $$x$$-axis$$\implies y=4$$.
Therefore, the co-ordinates of the required point are $$D(-6,4)$$.
Here, the ordinate is $$4$$.
Hence, option $$B$$ is correct.
Question 4
1 / -0

The point $$(-11, 0)$$ lies:

A
On the negative direction of $$y$$-axis

B
In the $$III$$ quadrant

C
On the negative direction of $$x$$-axis

D
In the $$IV$$ quadrant

Solution

Given, the point $$(-11,0)$$.

That is, $$x$$ is $$-11$$, which is negative and $$y$$ is $$0$$, i.e. the point lies on the $$x$$-axis.

Hence, the given point $$(-11,0)$$ lies on the negative direction of $$x$$-axis.

Therefore, option $$C$$ is correct.
Question 5
1 / -0

Signs of abscissa and ordinate of a point in the $$III$$ quadrant, respectively are

A
$$+, +$$

B
$$-, -$$

C
$$-, +$$

D
$$+, -$$

Solution

In $$III$$ quadrant, both $$x$$ and $$y$$ co-ordinates are negative.

So, option $$B$$ is correct.
Question 6
1 / -0

Point $$(0, -9)$$ lies

A
On the $$X$$-axis

B
In the $$II$$ quadrant

C
On the $$Y$$-axis

D
In the $$IV$$ quadrant

Solution
Question 7
1 / -0

Among all the points which has the largest abscissa in terms of magnitude?

A
$$B$$

B
$$D$$

C
$$C$$

D
$$G$$

Solution

Consider point is $$B$$.
Here, the point is at a distance of $$6$$ units right of the $$y$$-axis $$\implies x=6$$.
Also, the point is at a distance of $$1$$ unit above the $$x$$-axis$$\implies y=1$$.
Therefore, the co-ordinates of the required point are $$B(6,1)$$.
Here, the abscissa is $$6$$.
Hence, the magnitude of abscissa is $$6$$.

Consider point is $$D$$.
Here, the point is at a distance of $$6$$ units left of the $$y$$-axis $$\implies x=-6$$.
Also, the point is at a distance of $$4$$ unit above the $$x$$-axis$$\implies y=4$$.
Therefore, the co-ordinates of the required point are $$D(-6,4)$$.
Here, the abscissa is $$-6$$.
Hence, the magnitude of abscissa is $$6$$.

Consider point is $$C$$.
Here, the point is at a distance of $$4$$ units right of the $$y$$-axis $$\implies x=4$$.
Also, the point is at a distance of $$5$$ unit above the $$x$$-axis$$\implies y=5$$.
Therefore, the co-ordinates of the required point are $$G(4,5)$$.
Here, the abscissa is $$4$$.
Hence, the magnitude of abscissa is $$4$$.

Consider point is $$G$$.
Here, the point is at a distance of $$7$$ units left of the $$y$$-axis $$\implies x=-7$$.
Also, the point is at a distance of $$5$$ unit below the $$x$$-axis$$\implies y=-5$$.
Therefore, the co-ordinates of the required point are $$G(-7,-5)$$.
Here, the abscissa is $$-7$$.
Hence, the magnitude of abscissa is $$7$$.

Therefore, the only point which has the largest abscissa in terms of magnitude is $$G(-7,-5)$$.
Hence, option $$D$$ is correct.
Question 8
1 / -0

Point $$(-3, 7)$$ lies in the _____ quadrant

A
$$I$$

B
$$II$$

C
$$III$$

D
$$IV$$

Solution

In $$II$$ quadrant only $$x$$-coordinate is negative.
So, option $$B$$ is correct.
Question 9
1 / -0

If $$P (-2, 2), Q (3, -3), R (1, -1), S (-2, -3)$$ and $$T (-5, 5)$$ are plotted on the graph paper, then which points lie on $$II$$ quadrant?

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

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

C
Only $$S$$

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

Solution

We know, in the $$xy$$-plane, any point is of the form $$(x,y)$$, where $$x,y$$ can be any real number.

Also, for the point $$(x,y)$$,
in $$I$$ quadrant both $$x$$ and $$y$$ are positive,
in $$II$$ quadrant $$x$$ is negative and $$y$$ is positive,
in $$III$$ quadrant both $$x$$ and $$y$$ are negative
and in $$IV$$ quadrant $$x$$ is positive and $$y$$ is negative.

From the given points, only $$P(-2,2)$$ and $$T(-5,5)$$ has its $$x$$-coordinate negative and $$y$$-coordinate positive, and therefore these two points lie in the $$II$$nd quadrant.

Therefore, option $$A$$ is correct.
Question 10
1 / -0

Ordinate of a point is negative in _____ quadrant

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

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

C
$$III$$ and $$IV$$

D
$$IV$$ and $$I$$

Solution

Points that lie below the $$X$$-axis, have their $$y$$ co-ordinates negative.
Hence, $$III$$ and $$IV$$ quadrants have negative ordinates.
So, option $$C$$ is correct.

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Coordinate Geometry Test - 24

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Coordinate Geometry Test - 24

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Question 1

$$I$$

$$II$$

$$III$$

$$IV$$

Solution

Question 2

$$I$$ and $$II$$

$$II$$ and $$III$$

$$III$$ and $$IV$$

$$IV$$ and $$I$$

Solution

Question 3

$$-6$$

$$4$$

$$-2$$

$$10$$

Solution

Question 4

On the negative direction of $$y$$-axis

In the $$III$$ quadrant

On the negative direction of $$x$$-axis

In the $$IV$$ quadrant

Solution

Question 5

$$+, +$$

$$-, -$$

$$-, +$$

$$+, -$$

Solution

Question 6

On the $$X$$-axis

In the $$II$$ quadrant

On the $$Y$$-axis

In the $$IV$$ quadrant

Solution

Question 7

$$B$$

$$D$$

$$C$$

$$G$$

Solution

Question 8

$$I$$

$$II$$

$$III$$

$$IV$$

Solution

Question 9

$$P$$ and $$T$$

$$Q$$ and $$R$$

Only $$S$$

$$P$$ and $$R$$

Solution

Question 10

$$I$$ and $$II$$

$$II$$ and $$III$$

$$III$$ and $$IV$$

$$IV$$ and $$I$$

Solution

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