Coordinate Geometry Test

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Coordinate Geometry Test - 30

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Weekly Quiz Competition

Question 1
1 / -0

In which quadrant or on which axis each of the following points lie?
$$(- 3, 5), (4, -1), (2, 0), (2, 2), ( -3, -6)$$

A
$$IV, II, x$$-axis$$, I, III$$

B
$$II, IV, x$$-axis$$, I, III$$

C
$$IV, III, I, I, III$$

D
$$II, IV, y$$-axis$$, I, III$$

Solution

$$ Ans-\quad P\quad lies\quad in\quad the\quad II\quad quadrant.\\ \quad \quad \quad \quad Q\quad lies\quad in\quad the\quad IV\quad quadrant.\quad \\ \quad \quad \quad \quad R\quad lies\quad on\quad the\quad X-axis.\\ \quad \quad \quad \quad S\quad lies\quad in\quad the\quad I\quad quadrant.\quad \\ \quad \quad \quad \quad T\quad lies\quad in\quad the\quad III\quad quadrant.\\ \\ \\ \\ $$
Question 2
1 / -0

In the diagram, K, L, M & N are points on a

cartesian plane.

Which of the following points lie on both the

perpendicular bisectors of KL and MN?

A
(4, 0)

B
(4, 4)

C
(0, 4)

D
(4, 0)
Question 3
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:
$$B(10,4), C(0,4)$$ and $$D(0,-2)$$

A
$$(-10, 2)$$

B
$$(-10,-2)$$

C
$$(10,2)$$

D
$$(10,-2)$$

Solution

The given co-ordinates of the vertices of the rectangle $$ABCD$$ are $$B(10,4),\ C(0,4),\ D(0,-2)$$.
We need to plot $$A$$ on the graph.
Since, $$ABCD$$ is rectangle,
$$\therefore$$ The abscissa of $$A$$ will be same as that of $$B$$ and ordinate of $$A$$ will be same as that of $$D$$.
$$\therefore$$ Co-ordinates of $$A$$ are $$(10,-2)$$.
Hence, option $$D$$ is correct.
Question 4
1 / -0

In rectangle $$OABC$$; point $$O$$ is the origin, $$OA=10$$ units along $$x$$-axis and $$AB= 8$$ units. Find the co-ordinates of vertices $$A, B$$ and $$C$$.

A
$$A = ( 10,0 ), B =( 10, 8)$$ and $$C = (0, 8)$$

B
$$A = ( 10,0 ), C =( 10, 8)$$ and $$B = (0, 8)$$

C
$$B = ( 10,0 ), A=( 10, 8)$$ and $$C = (0, 8)$$

D
$$B = ( 10,0 ), C =( 10, 8)$$ and $$A = (0, 8)$$

Solution

We plot the point Origin $$O$$. Now, we move $$10$$ units to the right on the $$ x $$-axis and mark it as point $$A(10,0)$$.

Since $$OABC$$ is a rectangle, $$AB$$ will be perpendicular to $$OA$$. So, we move $$8$$ units upwards from $$A$$, and mark the point as $$B(10,8)$$.

Since opposite sides of the rectangle are equal , $$OA=BC$$ therefore move $$10$$ units to the left parallel to $$OA$$

Now we join $$OA, AB$$ and $$BC$$ with straight lines and complete the rectangle $$OABC$$. Hence, we obtain point $$C(0,8) $$.

Therefore, the coordinates $$A, B$$ and $$C$$ are $$(10,0), (10,8)$$ and $$(0,8)$$, respectively.

Hence, option $$A$$ is correct.
Question 5
1 / -0

The points (-2,0), (3,0), (3,5) and (-2,5) are the vertices of a:

A
rectangle

B
square

C
trapezium

D
kite

Solution

Let the given points be $$A = (-2, 0), B = (3, 0), C = (3, 5), D = (-2,5)$$.
Here clearly, the length of each side is equal and adjacent sides are perpendicular.
Therefore, the diagram formed by the given points is a square.

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

See figure and complete the following statements.
The x-coordinate and y-coordinate of the point $$L$$ are _______ and ______ respectively. Hence the coordinate of $$L$$ are ______

A
$$-5,-4,(-5,-4)$$

B
$$-5,-3,(-5,-4)$$

C
$$-5,4,(-5,-4)$$

D
$$5,-4,(-5,-4)$$

Solution

The point L is at a distance of $$4$$ units from the $$x - axis$$ and $$5$$ units from the $$y - axis$$.
It lies in the III quadrant
Hence, the abscissa or the $$x-coordinate$$ is $$-5$$, ordinate or the $$y-coordinate$$ is $$-4$$.
The point $$L$$ is $$(-5,-4)$$.
Question 7
1 / -0

In the graph, the coordinates of point $$S$$ are _____.

A
$$(-2,-2)$$

B
$$(-2,0)$$

C
$$(2,-2)$$

D
$$(2,2)$$

Solution

The required point is $$S$$.
Here, the point lies on the $$III$$rd quadrant.
The point is at a distance of $$2$$ unit left of the $$y$$-axis.
So, its abscissa will be $$-2$$.
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 $$S(-2,-2)$$.
Therefore, option $$A$$ is correct.
Question 8
1 / -0

The point $$(0, -6)$$ lies on:

A
$$y - axis (+ve)$$

B
$$x - axis(+ve)$$

C
$$x - axis (-ve)$$

D
$$y - axis (-ve)$$

Solution

Given, the point $$(0,-6)$$.
any point whose $$x$$-coordinate is $$0$$ and $$y$$-coordinate is non-zero will lie on the $$y$$-axis.
Here, $$x=0$$ and $$y=-6$$.Clearly, the point lies on the negative $$y$$-axis.
Hence, option $$D$$ is correct.
Question 9
1 / -0

In the graph, the coordinates of point $$Q$$ are _____.

A
$$(3,2)$$

B
$$(3,-2)$$

C
$$(-3,2)$$

D
$$(-2,3)$$

Solution

The required point is $$Q$$.
Here, the point lies on the $$IV$$th quadrant.
The point is at a distance of $$3$$ units right 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 $$Q(3,-2)$$.
Therefore, option $$B$$ is correct.
Question 10
1 / -0

In the graph, the coordinates of point $$R$$ are _____.

A
$$(1,1)$$

B
$$(-1,-1)$$

C
$$(-1,1)$$

D
$$(1,-1)$$

Solution

The required point is $$R$$.
Here, the point lies on the $$II$$nd quadrant.
The point is at a distance of $$1$$ unit left of the $$y$$-axis.
So, its abscissa will be $$-1$$.
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 $$R(-1,1)$$.
Therefore, option $$C$$ is correct.