Coordinate Geometry Test

Result

Coordinate Geometry Test - 19

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Question 1
1 / -0

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

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

We know, in the $$xy$$-plane, any point on the $$y$$-axis will have $$x =0$$.
Hence, any point on the $$y$$-axis is of the form $$(0,y)$$, where $$y$$ can be any non-zero number.

Therefore, any point whose $$x$$-coordinate is $$0$$ and $$y$$-coordinate is non-zero will lie on the $$y$$-axis.

That is, the statement is true.
Therefore, option $$A$$ is correct.
Question 2
1 / -0

State true or false:
The point $$(a, b)$$ lies on the $$y$$-axis if $$b= 0$$.

A
True

B
False

C
Depends

D
None

Solution

We know, in the $$xy$$-plane, any point on the $$y$$-axis will have $$x =0$$.
Hence, any point on the $$y$$-axis is of the form $$(0,y)$$, where $$y$$ can be any non-zero number.
But here, given the point $$(a,b)$$ and $$b=0$$.
Then, the point will be $$(a,0)$$.
Clearly, the point lies on the $$x$$-axis.
Hence, the given statement is false.
Therefore, option $$B$$ is correct
Question 3
1 / -0

Choose the correct option for the following statement.
The origin is in the first quadrant.

A
True

B
False

C
Ambiguous

D
Data insufficient

Solution

False.

The origin is the point of intersection of the x-axis and the y-axis. It does not lie in any of the quadrants. Hence, the given statement is False.
Question 4
1 / -0

The co-ordinates of the three vertices of a rectangle $$ABCD$$ are given. By plotting the given points, find the co-ordinates of the fourth vertex:
$$A(2,0), B(8,0)$$ and $$C(8,4)$$.

A
$$(4,2)$$

B
$$(8,0)$$

C
$$(8,8)$$

D
$$(2,4)$$

Solution

The given co-ordinates of the vertices of the rectangle $$ABCD$$ are $$A(2,0),\ B(8,0),\ C(8,4)$$.
We need to plot $$D$$ on the graph.
Since, $$ABCD$$ is rectangle,
$$\therefore$$ The abscissa of $$D$$ will be same as that of $$A$$ and ordinate of $$D$$ will be same as that of $$C$$.
$$\therefore$$ Co-ordinates of $$D$$ are $$(2,4)$$.
Thus, $$D=(2,4)$$.
Hence, option $$D$$ is correct.
Question 5
1 / -0

A Cartesian plane consists of two mutually _____ lines intersecting at their zeros.

A
perpendicular

B
parallel

C
at angle of $$60^o$$

D
at angle of $$30^o$$

Solution

The Cartesian plane consists of two perpendicular and directed lines whose intersection point is the zero point for both the lines.
Option A is correct.
Question 6
1 / -0

Write the coordinates of the point of intersection of $$x$$ - axis and $$y$$ - axis.

A
$$(5, 0)$$

B
$$(0, 5)$$

C
$$(1, 1)$$

D
$$(0, 0)$$

Solution

The coordinates of the point of intersection of $$x$$-axis and $$y$$-axis is $$(0,0)$$ which is also known as origin.

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

The co-ordinates of the three vertices of a rectangle $$ABCD$$ are given. By plotting the given points, find the co-ordinates of the fourth vertex:
$$A(-4,-6), C(6,0)$$ and $$D(-4,0)$$.

A
$$(-6, - 6)$$

B
$$(6,6)$$

C
$$(6,-6)$$

D
$$(-6,6)$$

Solution

The given co-ordinates of the vertices of the rectangle $$ABCD$$ are $$A(-4,-6),\ C(6,0),\ D(-4,0)$$.
We need to plot $$B$$ on the graph.
Since, $$ABCD$$ is rectangle,
$$\therefore$$ The abscissa of $$B$$ will be same as that of $$C$$ and ordinate of $$B$$ will be same as that of $$A$$.
$$\therefore$$ Co-ordinates of $$B$$ are $$(6,-6)$$.
Hence, option $$C$$ is correct.
Question 8
1 / -0

The co-ordinates of the three vertices of a rectangle $$ABCD$$ are given. By plotting the given points, find the co-ordinates of the fourth vertex:
$$A(4,2), B(-2,2)$$ and $$D(4,-2)$$.

A
$$(2, -2)$$

B
$$(-2,-2)$$

C
$$(2,2)$$

D
$$(-2,2)$$

Solution

The given coordinates of the vertices of rectangle $$ABCD$$ are $$A(4,2), B(-2,2), D(4,-2)$$.
We have to plot $$C$$ on the graph.
Since $$ABCD$$ is a rectangle, the abscissa of $$C$$ will be that of $$B$$ and the ordinate of $$D$$ will be that of $$C$$.
Therefore, the coordinate of $$C$$ will be $$(-2,-2)$$.
Hence, option $$B$$ is correct.
Question 9
1 / -0

The point $$(-3,2)$$ belongs to Quadrant ____________

A
$$I$$

B
$$II$$

C
$$III$$

D
$$IV$$

Solution

For the point $$(-3, 2)$$, $$x$$-coordinate $$=-3$$ is negative and $$y$$-coordinate $$= 2$$ is positive.
Hence the point will lie in the $$II$$ quadrant.
Question 10
1 / -0

The point $$(-2,0)$$ lies on:

A
$$+$$ve $$x$$-axis

B
$$+$$ve $$y$$-axis

C
$$-$$ve $$x$$-axis

D
$$-$$ve $$y$$-axis

Solution

Given, $$(-2,0)$$.
Since the $$y$$-coordinate is $$0$$, the point clearly lies on $$x$$-axis.
Also, the $$x$$-coordinate $$-2$$ being negative, the point lies on the negative $$x$$-axis.

Hence, option $$C$$ is correct.