ID : ae-9-Coordinate-Geometry [1]
Grade 9
Coordinate Geometry
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Answer t he quest ions
(1)
Point (1, 4) lies in which quadrant?
(2)
Find the resultant shape obtained by connecting points (35, -15) (5, -20) (15, -15) and (25, -20).
(3)
Which of the points A(9, 0), B(-6, 0), C(0, -19) and D(0, -17) lie on x axis.
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ID : ae-9-Coordinate-Geometry [2]
(4) Find the coordinates of the point shown in the picture.
(5)
Find the coordinates of points which lies on x-axis at a distance of 3 units f rom origin in the
negative direction of x-axis.
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ID : ae-9-Coordinate-Geometry [3]
Choose correct answer(s) f rom given choice
(6) Find the coordinates of the point shown in the picture.
a. (-40, 15)
b. (1.5, -4)
c. (-4, 1.5)
d. (15, -40)
(7) Signs of the abscissa and ordinate of a point in the second quadrant are respectively
(8)
a. + , +
b. - , -
c. +, -
d. - , +
T wo distinct __________ in a plane can not have more than one point in common.
a. Planes
b. Points
c. Both lines and points
d. Lines
(9) Find the coordinate of point whose abscissa is 5 and which lies on x-axis.
a. (1,5)
b. (5,1)
c. (0,5)
d. (5,0)
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ID : ae-9-Coordinate-Geometry [4]
(10) Bathshira and Bilal deposit some amount in joint back account such that total balance remains
2000. If amount deposited by Bathshira and Bilal are plotted as linear graph on x-y plane, f ind
the area between this graph and coordinate axes.
a. 4000000
b. 1000000
c. 3000000
d. 2000000
(11) A point both of whose coordinates are negative will lie in
a. First quadrant
b. T hird quadrant
c. Second quadrant
d. Fourth quadrant
(12) Find the distance of point (-4, -9) f rom y-axis.
a. 13
b. 4
c. 9
d. 0
(13) T wo distinct points in a plane determine _________ line.
a. Inf inite
b. T hree
c. One unique
d. T wo
(14) T he points in which abscissa and ordinate have same sign will lie in
a. Second and Fourth quadrants
b. Second and T hird quadrants
c. T hird and Fourth quadrants
d. First and T hird quadrants
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ID : ae-9-Coordinate-Geometry [5]
Fill in t he blanks
(15)
If coordinates of the point shown in the picture are (p+25, p+20), the value of p =
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ID : ae-9-Coordinate-Geometry [6]
Answers
(1)
First quadrant
Step 1
T here is a very simple mental map f or this.
You need to go in the anticlockwise direction f or this.
If both the numbers are positive (i.e. in the f orm (x,y), then the point lies in the f irst
quadrant.
If the f irst number is negative, and the second is positive (-x,y), it lies in the second
quadrant.
If both numbers are negative (-x,-y), it lies in the 3rd quadrant.
If the f irst is positive and the second is negative (x,-y), it lies in the 4th quadrant.
Step 2
Here the f irst number is positive, and the second is positive, so it lies in the First quadrant.
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ID : ae-9-Coordinate-Geometry [7]
(2)
Parallelogram
Step 1
We can draw these points and connect them on graph paper as f ollowing
Step 2
Now we notice f ollowing in this shape,
1. Opposite sides are equal
2. Opposite sides are parallel to each other.
Step 3
T hese are the properties of Parallelogram, theref ore this shape is a Parallelogram
(3)
A and B
A point lying on the X axis will have the abscissa as 0, and a point lying on the Y axis will
have the ordinate as 0.
Looking at the points here, we see points A and B will theref ore lies on the x axis
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ID : ae-9-Coordinate-Geometry [8]
(4) (2.5 , 1.5)
Step 1
In order to f ind the coordinates of the point shown in the picture, let's draw a horizontal
and a vertical line which connect this point to the y and x axis respectively.
Step 2
We can see that the vertical line intersects the x-axis at 2.5. T heref ore, the x-coordinate of
the point is 2.5.
Step 3
Similarly, the horizontal line intersects the y-axis at 1.5. T heref ore, the y-coordinate of the
point is 1.5.
Step 4
Hence the coordinates of the given point are (2.5, 1.5)
(5)
(-3, 0)
Note that if the point lies on the x-axis, then the y coordinate will be 0.
T he value of the x coordinate will be 3 if it lies in the positive direction, and -3 if it lies in the
negative direction.
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ID : ae-9-Coordinate-Geometry [9]
(6) a. (-40, 15)
Step 1
In order to f ind the coordinates of the point shown in the picture, let's draw a horizontal
and a vertical line which connect this point to the y and x axis respectively.
Step 2
We can see that the vertical line intersects the x-axis at -40. T heref ore, the x-coordinate of
the point is -40.
Step 3
Similarly, the horizontal line intersects the y-axis at 15. T heref ore, the y-coordinate of the
point is 15.
Step 4
Hence the coordinates of the given point are (-40, 15).
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ID : ae-9-Coordinate-Geometry [10]
(7) d. - , +
T he key to solving such questions is to build a mental map of the quadrants.
When both abscissa and ordinate are positive values (x,y), then the point is in the f irst
quadrant.
From there we go anticlockwise.
When abscissa is negative and ordinate is positive (-x,y), it is in quadrant two.
When both are negative (-x,-y), it is quadrant three.
When abscissa is positive and ordinate is negative, the point is in quadrant f our
(8)
d. Lines
Step 1
Following f igure shows the lines AB and CD, intersected at the point E.
Step 2
From the given f igure it is clear that, the two distinct lines can intersect at a single point
only and hence, we can say that the two distinct lines in a plane can not have more than
one point in common.
(9) d. (5,0)
T he key to note is that the f irst value that represents a point is called the abscissa, and the
second value is called the ordinate.
T he second point to remember is that if a point lies on the x-axis, then the ordinate value is
0.
Here we are given the abscissa value, and told that the point lies on the x axis, so the
answer is (5,0)
(10) d. 2000000
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ID : ae-9-Coordinate-Geometry [11]
(11) b. T hird quadrant
T here is a very simple mental map f or this.
You need to go in the anticlockwise direction f or this.
If both the numbers are positive (x,y), then the point lies in the f irst quadrant.
If the f irst number is negative , and the second is positive (-x,y), it lies in the second
quadrant.
If both numbers are negative (-x,-y), it lies in the 3rd quadrant.
If the f irst is positive and the second is negative (x,-y), it lies in the 4th quadrant.
Here both values are negative, theref ore it will lie in the T hird quadrant
(12) b. 4
T he simplest way to solve it is to remember that the abscissa - the f irst value - is the
position "on" the x axis, and the ordinate is the value "on" the y axis
What this means is that the f irst value is the distance away f rom the y axis, and the ordinate
is the distance away f rom the x axis.
Also remember to remove the sign - the distance is always positive
(13) c. One unique
Step 1
Following f igure shows a line, that is drawn through two distinct points A and B.
If we try to draw another line, it will not go through both A and B.
Step 2
T heref ore only one line can be drawn through two points
(14) d. First and T hird quadrants
T here is a very simple mental map f or this.
In the f irst quadrant, both the abscissa and ordinate (x,y) are positive.
In the second quadrant, the abscissa is negative , and the ordinate is positive (-x,y).
In the third quadrant, both numbers are negative (-x,-y).
In the f ourth quadrant, the abscissa is positive and the ordinate is negative (-x,-y).
Based on this, we f ind the answer to the question is First and T hird quadrants
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ID : ae-9-Coordinate-Geometry [12]
(15)
5
From observation we see that the point def ined is (30,25)
We are told that
30 = p + 25, and
25 = p + 20
From either of these equations we can see that p = 5
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