Coordinate Geometry Test

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Coordinate Geometry Test - 23

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Weekly Quiz Competition

Question 1
1 / -0

The perpendicular distance of point $$P(3, 4)$$ from $$x$$-axis is:

A
$$3$$

B
$$4$$

C
$$0$$

D
$$5$$

Solution

Given, $$P(3,4)$$.
Here, ordinate of $$P = 4$$, which is its perpendicular distance from $$x$$-axis.

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

What are the coordinates of $$Q$$?

A
$$(0,3)$$

B
$$(3,0)$$

C
$$(-3,0)$$

D
$$(0,-3)$$

Solution

The required point is $$Q$$.

Here, the point lies on $$y$$-axis.

Then, its abscissa is $$0$$ or $$x = 0$$.

Also, the point is at a distance of $$3$$ units above the $$x$$-axis

So, its ordinate will be $$+3$$.
Hence, the co-ordinates of the required point are $$Q(0,3)$$.
Therefore, option $$A$$ is correct.
Question 3
1 / -0

What are the coordinates of $$R$$?

A
$$(1,2)$$

B
$$(-1,2)$$

C
$$(1,-2)$$

D
$$(-2, 1)$$

Solution

The required point is $$R$$.

Here, the point lies on the $$II$$nd quadrant.

The point is at a distance of $$2$$ units left of the $$y$$-axis.
So, its abscissa will be $$-2$$.

Also, the point is at a distance of $$1$$ unit above the $$x$$-axis.

So, its ordinate will be $$1$$.
Hence, the co-ordinates of the required point are $$R(-2,1)$$.
Therefore, option $$D$$ is correct.
Question 4
1 / -0

What are the coordinates of $$S$$?

A
$$(3,2)$$

B
$$(3,-2)$$

C
$$(-2,3)$$

D
$$(-3,-2)$$

Solution

The point $$S$$ lies on the $$III^{rd}$$ quadrant.

The point is at a distance of $$3$$ units left of the $$y-$$axis.

So, its abscissa will be $$-3$$.

Also, the point is at a distance of $$2$$ unit below the $$x-$$axis.

So, its ordinate will be $$-2$$.

Hence, the co-ordinates of the required point are $$S(-3,-2)$$.
Question 5
1 / -0

Which of the following point lies in $$II$$ quadrant?

A
$$A$$

B
$$D$$

C
$$G$$

D
$$H$$

Solution

Consider point is $$A$$.
Here, the point is at a distance of $$2$$ units right of the $$y$$-axis.
So, its abscissa will be $$2$$.
Also, the point is at a distance of $$2$$ unit above the $$x$$-axis.
So, its ordinate will be $$2$$.
Therefore, the co-ordinates of the required point are $$A(2,2)$$.
Hence, the point lies on the $$I$$st quadrant.

Consider point is $$D$$.
Here, the point is at a distance of $$6$$ units left of the $$y$$-axis.
So, its abscissa will be $$-6$$.
Also, the point is at a distance of $$4$$ unit above the $$x$$-axis.
So, its ordinate will be $$4$$.
Therefore, the co-ordinates of the required point are $$D(-6,4)$$.
Hence, the point lies on the $$II$$nd quadrant.

Consider point is $$G$$.
Here, the point is at a distance of $$7$$ units left of the $$y$$-axis.
So, its abscissa will be $$-7$$.
Also, the point is at a distance of $$5$$ unit below the $$x$$-axis.
So, its ordinate will be $$-5$$.
Therefore, the co-ordinates of the required point are $$G(-7,-5)$$.
Hence, the point lies on the $$III$$rd quadrant.

Consider point is $$H$$.
Here, the point is at a distance of $$5$$ units right of the $$y$$-axis.
So, its abscissa will be $$5$$.
Also, the point is at a distance of $$3$$ unit below the $$x$$-axis.
So, its ordinate will be $$-3$$.
Therefore, the co-ordinates of the required point are $$H(5,-3)$$.
Hence, the point lies on the $$IV$$th quadrant.

Therefore, the only point that lies in the $$II$$nd quadrant is $$D(-6,4)$$.

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

What are the co-ordinates of $$O$$?

A
$$(1,1)$$

B
$$(1,0)$$

C
$$(0,0)$$

D
$$(0,1)$$

Solution

We know, the coordinates of the point of intersection of $$x$$ - axis and $$y$$ - axis is called the origin.

That is, the co-ordinates of the origin is $$(0,0) $$.

Therefore, option $$C$$ is correct.
Question 7
1 / -0

Which of the following point lies on $$Y$$-axis?

A
$$P$$

B
$$Q$$

C
$$R$$

D
$$S$$

Solution

Consider point is $$P$$.

Here, the ordinate is $$0$$ or $$y = 0$$.

Also, the point is at a distance of $$2$$ units right of the $$y$$-axis.

So, its abscissa will be $$+2$$.

Therefore, the point lies on the $$x$$-axis.

Hence, the co-ordinates of the required point are $$P(2,0)$$.

Consider point is $$Q$$.

Here, the abscissa is $$0$$ or $$x = 0$$.

Also, the point is at a distance of $$3$$ units above the $$x$$-axis

So, its ordinate will be $$+3$$.

Therefore, the point lies on the $$y$$-axis.

Hence, the co-ordinates of the required point are $$Q(0,3)$$.

Consider point is $$R$$.

Here, the point is at a distance of $$2$$ units left of the $$y$$-axis.

So, its abscissa will be $$-2$$.

Also, the point is at a distance of $$1$$ unit above the $$x$$-axis.

So, its ordinate will be $$1$$.

Therefore, the point lies on the $$II$$nd quadrant.
Hence, the co-ordinates of the required point are $$R(-2,1)$$.

Consider point is $$S$$.

Here, the point is at a distance of $$3$$ units left of the $$y$$-axis.

So, its abscissa will be $$-3$$.

Also, the point is at a distance of $$2$$ unit below the $$x$$-axis.

So, its ordinate will be $$-2$$.

Therefore, the point lies on the $$III$$rd quadrant.
Hence, the co-ordinates of the required point are $$S(-3,-2)$$.

Therefore, the only point that lies on the $$y$$-axis is $$Q(0,3)$$.

Hence, option $$B$$ is correct.
Question 8
1 / -0

The coordinates of a point, if its distance from $$x$$-axis is $$10$$ and from negative $$y$$-axis is $$2$$ are:

A
$$(10, 2)$$

B
$$(10, -2)$$

C
$$(-2, 10)$$

D
$$(2, 10)$$

Solution

Here,
Abscissa $$= 2$$ $$ (\because$$ Distance from $$y$$-axis).
Ordinate $$= 10 $$ $$(\because $$ Distance from $$x$$-axis).

Therefore, the coordinates of the required point are $$(2,-10)$$, which is shown in the figure.

Hence, option $$D$$ is correct.
Question 9
1 / -0

What are the coordinates of $$\text{P}$$?

A
$$(0,2)$$

B
$$(2,0)$$

C
$$(-2,0)$$

D
$$(0,-2)$$

Solution

The required point is $$\text{P}$$.

Here, the point lies on $$x$$-axis.

Then, its ordinate is $$0$$ i.e. $$y = 0$$.

Also, the point is at a distance of $$2$$ units right of the $$y$$-axis.

So, its abscissa will be $$+2$$.
Hence, the coordinates of the required point are $$\text{P}(2,0)$$.

Therefore, option $$\text{B}$$ is correct.
Question 10
1 / -0

Which of the given points lie in quadrant $$\text{IV} $$:
$$P (-2, 2), Q (3, -3), R (1, -1), S (-2, -3)$$ and $$T (-5, 5)$$

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

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

C
Only $$S$$

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

Solution

For points in quadrant $$\text{IV}$$:
$$x$$ co-ordinate is positive
$$y$$ co-ordinate is negative

Points $$Q(3,-3)$$ and $$R(1,-1)$$ have positive $$x$$ coordinate and negative $$y$$ coordinate.

So, option $$B$$ is correct.