Are you looking for Coordinate Geometry Extra Questions and Answers, if yes? then you the right place. Here we are providing Coordinate Geometry Extra Questions and Answers Class 9 Maths Chapter 3.
Coordinate Geometry Extra Questions and Answers Maths Chapter 3
- 1 mark question-
1) The co-ordinates of the origin are…
a) (2, 0)
b) (0, 2)
c) (0, 0)
d) (2, 2)
Ans-c
2) The point C(-7 -3) lies in
a) III Quadrant
b) IV Quadrant
c) I Quadrant
d) II Quadrant
Ans-a
3) The point (4, 0) lies on :
a) +ve x-axis
b) +ve y-axis
c) –ve x-axis
d) –ve y-axis
Ans-a
4) The coordinates of a point on the x- axis of the form are… .. ..
a) (0, 0)
(b) (x, y)
(c) (0, y)
(d) (x, 0)
Ans-d
5) . If the y-coordinate of a point is zero, then this point lies:
a) In II quadrant
b) In I quadrant
c) On x-axis
d) On y-axis
Ans-c
6) The point of intersection of vertical and horizontal lines determining the position of point in a cartesian plane is called:
a) y-axis
b) X-axis
c) origin
d) Quadrants
Ans-c
7) The perpendicular distance of a point P (4,9) from the y-axis is:
a) 4
b) 8
c) 9
d) 13
Ans-a
8) The positive point of Abscissa in… ..
a.) I quadrant
b.) I and II quadrants
c.) II quadrant only
d.) I and IV quadrants
Ans-d
9) The slope intercept form of a line is… ..
a) y = mx+c
b) y1 = mx1 + c
c) 0
d) y=mx^2
Ans-a
10) The correct midpoint formula is ,
a) M(x, y) =[1/2(x1-x2), 1/2[(y1-y2)]
Ans – a
11) Points (2,3), (-3,-3), (4,-3);
a) First quadrant
b) M (x, y) = [1/2(x1 + x2), 1/2[(y1 + y2)]
c) M(x, y) =[1/2(x1+x2), ½[y1+y2]
d) none of these
Ans-b
12) The cartesian plane is divided into four equal parts, called quadrants.
a) true
b) false
Ans-a
13) Point (3,2), (-4,-3), (3,-3);
a) First quadrant
b) Do not lie in the same quadrant
c) Third quadrant
d) Fourth quadrant
Ans-b
14) A point (x + 3, x + 6) lies in the first quadrant, the mirror image for which for x-axis is (3, –5). What is the value of x?
a) (–3, –5)
b) (–3, 5)
c) (3, –5)
d) (3, 5)
Ans-d
15) The plane is called the Cartesian, or Coordinate plane and the lines are called the coordinate.
a) true
b) false
Ans-a
16) The Coordinate axes divide the plane into four parts Called quadrants.
a) quadrant
b) parts
c) plane
d) quadients
Ans-a
17) define x-axis
Ans=>The name of the horizontal line in the cartesian plane which determines the position of a point is called x-axis.
18) The point (-9, 0) lies in
(a) Fourth quadrant
(b) On the negative direction of the x-axis
(c) On the negative direction of the y-axis
(d) Origin
Ans-c
- 2 marks questions
1) Write the coordinates of each of the points P, Q, R, S, T and O from the figure given.
=>The coordinates of the points P, Q, R, S, T and O are as listed below
P = (1, 1)
Q = (2, 1)
R = (-2, -4)
S = (-3, -1)
T = (3, -2)
O = (0, 0)
2) Without plotting the points indicate the quadrant in which they will lie, if
(i) The ordinate is 4 and abscissa is – 2
(ii) The abscissa is – 4 and ordinate is – 2
(iii) The abscissa is – 5 and ordinate is 3
(iv) The ordinate is 5 and abscissa is 3
Ans=> The point is (-2,4).
Hence, the point lies in the || quadrant.
(i) The point is (-4,-2).
Hence, the point lies in the III quadrant.
(ii) The point is (-5,3).
Hence, the point lies in the II quadrant.
(iii) The point is (3,5).
Hence, the point lies in the I quadrant.
3) Find distances of points P(-4, -2) and Q(5, 2) from x-axis and y-axis.
Ans=>
Distances of point P(-4, -2) from x-axis is 2 units in the negative direction and from y-axis is 3 units in the negative direction. Distances of point Q(5, 2) from x-axis is 2 units and from y-axis is 5 units.
4) In the given figure, PQR is an equilateral triangle with coordinates of Q and R as (-2, 0) and (2, 0) respectively. Find the coordinates of the vertex P.
Ans=>
Here,
QR = OQ + OR.
= 3+ 2 = 5 units
∆PQR is an equilateral triangle.
PQ = PR = QR = 5 units
In right-angled ∆OPQ, <POQ = 90°
We have PQ2 = OP2 + OQ2
OP2 = PQ2 – OQ2
52 – 22 = 25 – 4 = 21
OP = 21
5) Find the values of x and y, if two ordered pairs (x – 4, – 6) and (3, x + y) are equal.
Ans=>
Here,
two ordered pairs are equal.
Their first components are equal and their second components are separately equal.
x – 4 = 3 and x + y = -6
x = 7 and 7 + y = -6 ⇒ y = – 13
Hence, x = 7 and y = – 13.
6) In which quadrant or on which axis do each of the points (-5, 4), (3, -2), (-3, 0), (3, 2) and (-4,-5) lie?
Ans=>
(-5, 4): Second Quadrant
(3,-2) Fourth Quadrant
(-3,0): x-axis
(3, 2): First Quadrant
(-4,-5): Third Quadrant
7) Plot the following ordered pairs (x, y) of numbers as points in the Cartesian Plane. Use the scale 1cm = 1 unit on the axes.
X |
-2 | 0 | -3 | 5 | 3 |
Y | 5 | -3 | -4 | 5 |
-2 |
Ans=>
- 5 marks question-
1) Plot the following points and check whether they are collinear or not:
(i) (1, 4), (– 2, – 2), (– 3, – 4)
(ii) (1, 1), (2, – 3), (– 4, 2)
(iii) (0, 0), (3,3), (4, 4)
=>
Hence, the points are collinear.
The point(1, 4), (– 2, – 2), (– 3, – 4) lie in a straight line,
2) (1, 1), (2, – 3), (– 4, 2)
The points (1, 1), (2, – 3), (– 4, 2) do not lie in a straight line,
Hence, the points are not collinear.
3) (0, 0), (3, 3), (4, 4)
The points (0, 0), (3, 3), (4, 4) lie in a straight line,
Hence, the points are collinear.
2) solve the following equation.
a) 2x+4=20
=>2x=20-4
2x=16
X=16/4
X=4
b) 6u+21/4=3u+7
=>6u-3u=7-21/4
3u=(7×4-21) /4
3u=(28-21) /4
3u=7/4
U=7/4×1/3
U= 7/12
c) 2x – (3x – 4) = 3x – 5
2x – 3x + 4 = 3x – 5
2x-3x – 3x = – 5-4
-4x=-9
X = -9/-4
X=9/4
d) 2x + √2 = 3 x-4-3√2
2x – 3x = -4-3√2-√2
x = -(4+ 4√2)
.x = 4+4√2
e) 2y + 7 = 19
2y = 19-7
2y = 12
y = 12/2
y = 6
3) Find out which of the following equations have x = 2, y = 1 as a
a) 2x + 5y = 9
ans=>2(2) +5y=9
4+5y=9
5y=9-4
Y=1
4) Find out which of the following equations have x = 2, y = 1 as a
a) 3x + 5y = 9
b) 5x+3y = 14
c) 2x + 3y = 7
d) 4x – 3y=1
e) 3x – 3y +7= 8
Answer=
a) 3x + 5y = 9
When x = 2
3×2+5y = 9
5y = 9-6
5y = 3
y = 3/5
x = 2, y = 1 is not a solution of this equation.
b) 5x + 3y = 14
When x = 2,
5×2 + 3y = 14
3y = 14 -10
y = 4/3
x = 2, y = 1 is not a solution of this equation.
c) 2x-3y +7=8
When x = 2,
2×2-3y + 7 = 8
-3y=8-4-7
-3y = -3
y = 1
X = 2, y = 1 is a solution of this equation.
D) 4x – 3y=1
4×2-3y=1
8-3y=1
3y=-7
Y=7/3
X=2, y=1 is not a solution of this equation
e) 3x – 3y +7= 8
3(2) -3y+7=8
6-3y=8-7
6-3y=1
3y=1-6
3Y=-5
Y =5/3
X=2, y=1 is not a solution of this equation