ID : ph-9-Coordinate-Geometry [1]
Grade 9
Coordinate Geometry
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Answer t he quest ions
(1)
Find the coordinate of point whose abscissa is 1 and which lies on x-axis.
(2)
Find the distance of point (6, 3) f rom y-axis.
(3)
Find the resultant shape obtained by connecting points (5, 5) (-30, -5) (-25, 5) and (0, -5).
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ID : ph-9-Coordinate-Geometry [2]
(4) Find the coordinates of the point shown in the picture.
Choose correct answer(s) f rom given choice
(5)
T he points in which abscissa and ordinate have dif f erent signs will lie in
a. First and Second quadrants
b. Second and Fourth quadrants
c. First and Fourth quadrants
d. First and T hird quadrants
(6) Signs of the abscissa and ordinate of a point in the f irst quadrant are respectively
a. - , -
b. - , +
c. +, -
d. + , +
(7) T wo distinct points in a plane determine _________ line.
a. One unique
b. T hree
c. T wo
d. Inf inite
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ID : ph-9-Coordinate-Geometry [3]
(8)
Find the coordinates of the point shown in the picture.
a. (15, 30)
b. (1.5, 3)
c. (3, 1.5)
d. (30, 15)
(9) Find the coordinates of points which lies on y-axis at a distance of 5 units f rom origin in the
negative direction of y-axis.
a. (-5, 0)
b. (0, -5)
c. (0, 5)
d. (5, 0)
(10) T wo distinct __________ in a plane can not have more than one point in common.
a. Planes
b. Points
c. Lines
d. Both lines and points
(11) Point (10, 10) lies in which quadrant?
a. Second quadrant
b. T hird quadrant
c. First quadrant
d. Fourth quadrant
(12) A point both of whose coordinates are positive will lie in
a. Second quadrant
b. T hird quadrant
c. Fourth quadrant
d. First quadrant
(13) Which of the points P(0, 19), Q(0, 3), R(8, 0) and S(12, 0) lie on y axis.
a. Q and R
b. Q and P
c. R and S
d. P and S
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ID : ph-9-Coordinate-Geometry [4]
Fill in t he blanks
(14) Reynante and Bituin deposit some amount in joint back account such that total balance remains
100. If amount deposited by Reynante and Bituin are plotted as linear graph on x-y plane, the
area between this graph and coordinate axes =
(15)
.
If coordinates of the point shown in the picture are (p+10, p+60), the value of p =
.
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ID : ph-9-Coordinate-Geometry [5]
Answers
(1)
(1,0)
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 (1,0)
(2)
6
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
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ID : ph-9-Coordinate-Geometry [6]
(3)
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
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ID : ph-9-Coordinate-Geometry [7]
(4) (-1.5 , -3)
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 -1.5. T heref ore, the x-coordinate
of the point is -1.5.
Step 3
Similarly, the horizontal line intersects the y-axis at -3. T heref ore, the y-coordinate of the
point is -3.
Step 4
Hence the coordinates of the given point are (-1.5, -3)
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ID : ph-9-Coordinate-Geometry [8]
(6) 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
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ID : ph-9-Coordinate-Geometry [9]
(8)
a. (15, 30)
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 15. T heref ore, the x-coordinate of
the point is 15.
Step 3
Similarly, the horizontal line intersects the y-axis at 30. T heref ore, the y-coordinate of the
point is 30.
Step 4
Hence the coordinates of the given point are (15, 30).
(9) b. (0, -5)
Note that if the point lies on the y-axis, then the x coordinate will be 0.
T he value of the y coordinate will be 5 if it lies in the positive direction, and -5 if it lies in the
negative direction.
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ID : ph-9-Coordinate-Geometry [10]
(10) c. 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.
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ID : ph-9-Coordinate-Geometry [11]
(11) c. 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.
(12) d. First 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 positive, theref ore it will lie in the First quadrant
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ID : ph-9-Coordinate-Geometry [12]
(13) b. Q and P
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 Q and P will theref ore lies on the y axis
(14)
(15)
5000
-30
From observation we see that the point def ined is (-20,30)
We are told that
-20 = p + 10, and
30 = p + 60
From either of these equations we can see that p = -30
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