Question Set C

CBSE 9th Standard Mathematics Coordinate Geometry Important Questions And Answers Study Material - QB365

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Questions:

Generic 3

10 x 3 = 30

Draw a quadrilateral whose vertices are (3, 2), (2, 3), (-4, 5) and (5, -4).

In which quadrants do the following points lie?
(i) (5, -3)
(ii) (-8, 4)
(iii) (-3, -6)
(iv) (5, 4)

Look at the following figure and fill in the blanks:
(i) The abscissa and the ordinate of the point B are ____ and ____ respectively. Hence, the coordinates of B are (____, ____).
(ii) The x-coordinate and the y-coordiante of the point A are ____ and ____ respectively. Hence, the coordinates of A are (____, ____).
(iii) The x-coordinate and the y-coordinate of the point D are ____ and ____ respectively. Hence, the coordinates of D are (____, ____).

Write the coordinates of the vertices of a rectangle, whose length and breadth are 6 units and 3 units respectively, one vertex at the origin, the longer side lies on the Y-axis and one of the vertices lies in the II quadrant. Also, find the area of the rectangle.

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

A point lies on X-axis at a distance of 9 units from Y-axis. What are its coordinates? What will be the coordinates of a point, if it lies on Y-axis at a distance of 9 units from X-axis in negative direction?

If the coordinates of two points are A(3,4) and B(-2,5), then find (Abscissa of A) - (Abscissa of B).

If the coordinates of a point M are (2,9) which can also be expressed as (1 + x,y²) and y > 0, then find in which quadrant do the following points lie: P(x,y), Q(2,x), R(x²,y-1), S(2x,-3y)

Locate and write the coordinates of a point:
(a) above x-axis lying on y-axis at a distance of 5 units from origin.
(b) below x-axis lying on y-axis at a distance of 3 units from origin.
(e) lying on x-axis to the right of origin at a distance of 5 units.
(d) lying on x-axis to the left of origin at a distance of 2 units.

10.

(Street Plan):A city has two main roads cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.All the other streets of the city run parallel to these roads and are 200 m apart.There are 5 streets in each direction.Using 1 cm = 200 m, draw a model of the city on your notebook.Represent the roads/streets by single line.

There are many cross-streets in your model.A particular cross-street is made by two streets, one running in the North-South direction and another in the East- West direction.Each cross-street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5).Using this convention, find:
(i) how many cross-streets can be referred to as (4,3)?
(ii) how many cross-streets can be referred to as (3,4)?

Generic 2

10 x 2 = 20

11.

In which quadrant does a point lie. whose both coordinates are negative?

12.

Find the distance of point 5(-3,6) from Y-axis.

13.

Plot the points A(6,6), B(4,4), C(-1,-1) in the Cartesian plane and show that the points are collinear.

14.

(i) Plot the points A(0,4), B(-3,0), C(0,-4), D(3,0)
(ii) Name the figure obtained by joining the points A, B, C, D.
(iii) Also, name the quadrants in which sides AB and AD lie.

15.

Plot the points A(-3,-3), B(3,-3), C(3,3), D(-3,3) in the Cartesian plane.Also, find the length of the line segment AB.

16.

Observe figure and answer the following:

(a) coordinates of B
(b) point identified by the coordinates (-2, -3)
(c) abscissa of point D
(d) ordinate of point H
(e) points with the same abscissa
(f) points with the same ordinate

17.

The perpendicular distance of a point from the x-axis is 4 units and the perpendicular distance from the y-axis is 5 units.Write the coordinates of such a point if lies in the:
(i) I quadrant
(ii) II quadrant
(iii) III quadrant
(iv) IV quadrant

18.

Find the coordinates of the point which lies on y-axis at a distance of 4 units in negative direction of y-axis.
(a) (-4,0) (b) (4,0) (c) (0,-4) (d) (0,4)

19.

In which quadrant do the given point lie? (-4,-5)

20.

In which quadrant do the given point lie? (2,-1)

Multiple Choice Question

10 x 1 = 10

21.

In which quadrant does the point (1,-2) lie?

(a)

(b)

(c)

III

(d)

22.

Abscissa of a point is positive in:

(a)

I and II quadrants

(b)

I and IV quadrants

(c)

I quadrant only

(d)

IV quadrant only

23.

In fourth quadrant, y is

(a)

-ve

(b)

+ve

(c)

(d)

None of these

24.

Where do the four quadrants meet?

(a)

at O

(b)

in x - axis

(c)

in y axis

(d)

do not meet

25.

Where do the I and III quadrants meet?

(a)

in x - axis

(b)

in y - axis

(c)

at O

(d)

do not intersect

26.

The line of intersection of IV and I quadrants is

(a)

x - axis

(b)

y - axis

(c)

vertical axis

(d)

None of these

27.

The line of intersection of I and III quadrants is

(a)

x - axis

(b)

y - axis

(c)

horizontal axis

(d)

None of these

28.

If x is negative and y is positive, then the point (x,y) lies in

(a)

II quadrant

(b)

III quadrant

(c)

IV quadrant

(d)

I quadrant

29.

Which of the following is an example of a geometrical line?

(a)

Black Board

(b)

Sheet of paper

(c)

Meeting place of two walls

(d)

Tip of the sharp pencil

30.

Rene Descartes was a

(a)

French mathematician

(b)

Indian mathematician

(c)

Russian mathematician

(d)

British mathematician

Generic 5

2 x 5 = 10

31.

KGB schools provide free education to girls students from weaker sections. The local body of a town want to open a KGB school in the town for which a rectangular plot ABCD, as shown in the following figure, is very suitable. But this plot belongs to Rati Ram. Rati Ram agrees to exchange it with triangular plot PQR as shown in the same figure. The co-ordinates of the vertices of both the plots are shown in the figure:

(i) Compare the areas of both the plots.
(ii) Which mathematical concept is used in the above problem?
(iii) By opening KGB school in the town, which value is depicted by the local body?

32.

See the figure given below and write the following:
(i) The co-ordinates of B.
(ii) The co-ordinates of C.
(iii) The point identified by the co-ordinates (-3, -5).
(iv) The point identified by the co-ordinates (2, -4).
(v) The abscissa of the point D.
(vi) The ordinate of the point H
(vii) The co-ordinates of the point L.
(viii) The co-ordinates of the point M.

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Answers Key:

Generic 3

10 x 3 = 30

First, we draw the coordinate axes XOX' and YOY'. Now let the vertices of the required quadrilateral are A(3, 2), B(2, 3), C(-4, 5) and D(5, -4).
Therefore, plot the point A, B, C and D and join them.
We get the quadrilateral ABCD as shown in the following figure.

(i) ∴ Points of type (+, -) lie in the 4th quadrant.
∴ Point (5, -3) lies in the quadrant IV.
(ii)∴ Points of the type h+) lie in the 2nd quadrant.
∴ The point (-8, 4) lies in the quadrant II.
(iii)∴ The points of the type (-, -) lie in the 3rd quadrant.
∴ The point (-3, --6) lies in the quadrant III.
(iv) ∴ The points of the type (+, +) lie in the 1st quadrant.
∴ The point (5, 4) lies in the quadrant I.

(i) The abscissa and the ordinate of the point B are -3 and 3 respectively. Hence, the coordinates of B are (-3, 3).
(ii) The x-coordinate and the y-coordinate of the point A are 4 and 2 respectively. Hence the coordinates of A are (4,2).
(iii) The x-coordinate and y-coordiante of the point D are 6 and -2 respectively. Hence, the coordinates of D are (6,-2).

Let us draw the coordinate axes XOX' and YOY " and choose a suitable units of distance on the axes.
Let 1 cm = 1 unit.
Mark a point A on Y-axis at a 6 units distance in positive direction of Y-axis and mark a point C on X-axis at a 3 units distance in negative direction of X-axis.

Now, draw a perpendicular lines from C and A, which meets at a point B. Thus, we get the rectangle OABC whose vertices are O(0,0), A(0, 6), B(-3, 6) and C(-3, 0), respectively.
.\(\because \) Area of the rectangle = Length x Breadth
\(\therefore \) Area of rectangle OABC = 6 x 3 = 18 sq units

(i) For point (-3, 5), x-coordinate is negative and y-coordinate is positive, so it lies in II quadrant.
(ii) For point (4, -1), x-coordinate is positive and y-coordinate is negative, so it lies in IV quadrant.
(iii) For point (2, 0), x-coordinate is positive and y-coordinate is zero, so it lies on X-axis.
(iv) For point (2, 2), x-coordinate and y-coordinate both are positive, so it lies in I quadrant.
(v) For point (-3, - 6), x-coordinate and y-coordinate both are negative, so it lies in III quadrant.

We know that, coordinates of any point lies on X-axis atthe distance' a' from the Y -axis are (a, 0) and (- a, 0). Since, the given point lies on X-axis at a distance of9 units from Y-axis, so its coordinates are (9, O)or (- 9, 0). Now, if point lies on Y-axis at a distance of9 units from X-axis in negative direction, then its coordinates are (0, 9) and (0, - 9).

Given, Point A (3, 4) i.e. abscissa of A = 3
and Point B (- 2, 5), i.e. abscissa of B = - 2
\(\therefore\) Abscissa of A - Abscissa of B
= 3 - (-2) = 3 + 2 = 5

\(P\rightarrow I\)
\(\\ Q\rightarrow I\)
\(\\ R\rightarrow I\)
\(\\ S\rightarrow IV\)

(a) (0,5)
(b) (0,-3)
(c) (5,0)
(d) (-2,0)

10.

Both the cross-streets are marked in the figure given.They are uniquely found because of the two reference lines we have used for locating them.

Generic 2

10 x 2 = 20

11.

III quadrant

12.

The distance of a point 8(-3, 6) from Y-axis is equal to x-coordinate of S. i.e. 3 units.

13.

14.

(i)

(ii) Rhombus
(iii) II, I

15.

6 Units.

16.

(a) (2,3)
(b) A
(c) 0
(d) 0
(e) M, O, D, H; B, G
(f) M, H, O

17.

(i) (5,4) (ii) (-5,4) (iii) (-5,-4) iv (5,-4)

18.

19.

III

20.

Multiple Choice Question

10 x 1 = 10

21.

(d)
IV

22.

(b)
I and IV quadrants

23.

(a)
-ve

24.

(a)
at O

25.

26.

(a)
x - axis

27.

(b)
y - axis

28.

(a)
II quadrant

29.

30.

(a)
French mathematician

Generic 5

2 x 5 = 10

31.

(i) For rectangle ABCD:
AB = 8 - 2 = 6 units ← Length
AD = 12 - 8 = 4 units ← Breadth
∴ Area of rectangle ABCD = AB x AD
= 6 units x 4 units
= 24 sq. units.
For triangle PQR:
QR = 12 - 4 = 8 units ← Base
SP = 6 - 0 = 6 units ← Height
∴ Area of ΔPQR = \(\frac{1}{2}\) base x height
= \(\frac{1}{2}\) x 8 x 6 sq. units
= 24 sq. units.
⇒ \(\left[\begin{array}{l} \text { area of } \\ \text { rect. } \mathrm{ABCD} \end{array}\right]=\left[\begin{array}{l} \text { area of } \\ \Delta \mathrm{PQR} \end{array}\right]\)
(ii) Co-ordinate Geometry.
(iii) Community or social upliftment.

32.

From the figure, we have
(i) The co-ordinates of B are (-5, 2).
(ii) The co-ordinates of C are (5, -5).
(iii) The point E is identified by the co-ordinates (-3, -5)
(iv) The point G is identified by the co-ordinates (2, -4).
(v) The abscissa of the point D is 6.
(vi) The ordinate of the point H is -3.
(vii) The co-ordinates of the point L are (0, 5).
(viii) The co-ordinates of the point M are (-3, 0).
Plotting a point in the plane when coordinates of the point are given
To plot a point in the coordinate plane we draw the coordinate axes and choose our units such that we can mark equal distances on the x-axis or on the y-axis or on both the axes. We take origin as zero for x-axis as well as on y-axis. The distances marked along OX and OY are taken as positive and those along OX and OY are taken as negative.

CBSE 9th Standard Mathematics Coordinate Geometry Important Questions And Answers Study Material - QB365 Set C

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Std: 9th Standard CBSE - Mathematics

chapter: Coordinate Geometry - Important Questions And Answers

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Questions:

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Answers Key:

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