Download Grade 9 Coordinate Geometry

ID : us-9-Coordinate-Geometry [1]
Grade 9
Coordinate Geometry
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Answer t he quest ions
(1)
Find the distance of point (-1, -2) f rom x-axis.
(2)
Mason and Makayla deposit some amount in joint back account such that total balance remains
700. If amount deposited by Mason and Makayla are plotted as linear graph on x-y plane, f ind
the area between this graph and coordinate axes.
(3)
Which of the points J(3, 0), K(0, 6), L(0, 7) and M(-12, 0) lie on y axis.
(4) Find the coordinates of the point shown in the picture.
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ID : us-9-Coordinate-Geometry [2]
(5)
Find the resultant shape obtained by connecting points (30, 5) (5, 5) (30, 15) and (5, 15).
Choose correct answer(s) f rom given choice
(6) 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.
a. (0, -3)
b. (-3, 0)
c. (0, 3)
d. (3, 0)
(7) Signs of the abscissa and ordinate of a point in the second quadrant are respectively
(8)
a. - , -
b. +, -
c. + , +
d. - , +
T wo distinct points in a plane determine _________ line.
a. Inf inite
b. T hree
c. T wo
d. One unique
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ID : us-9-Coordinate-Geometry [3]
(9) Find the coordinates of the point shown in the picture.
a. (-1.5, 4)
b. (4, -1.5)
c. (40, -15)
d. (-15, 40)
(10) T wo distinct __________ in a plane can not have more than one point in common.
a. Points
b. Planes
c. Lines
d. Both lines and points
(11) A point both of whose coordinates are positive will lie in
a. Second quadrant
b. Fourth quadrant
c. T hird quadrant
d. First quadrant
(12) Point (-10, -2) lies in which quadrant?
a. T hird quadrant
b. Fourth quadrant
c. First quadrant
d. Second quadrant
(13) Find the coordinate of point whose ordinate is 6 and which lies on y-axis.
a. (6,0)
b. (1,6)
c. (0,6)
d. (6,1)
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ID : us-9-Coordinate-Geometry [4]
(14) If coordinates of the point shown in the picture are (p+80, p+15), f ind the value of p.
a. -40
b. -50
c. -45
d. -55
(15) T he points in which abscissa and ordinate have same sign will lie in
a. First and Second quadrants
b. T hird and Fourth quadrants
c. Second and Fourth quadrants
d. First and T hird quadrants
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ID : us-9-Coordinate-Geometry [5]
Answers
(1)
2
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
(2)
245000
(3)
L and K
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 L and K will theref ore lies on the y axis
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ID : us-9-Coordinate-Geometry [6]
(4) (3 , -1)
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 3. T heref ore, the x-coordinate of
the point is 3.
Step 3
Similarly, the horizontal line intersects the y-axis at -1. T heref ore, the y-coordinate of the
point is -1.
Step 4
Hence the coordinates of the given point are (3, -1)
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ID : us-9-Coordinate-Geometry [7]
(5)
Rectangle
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 and parallel to each other
2. All angles are equal and are right angles (90°).
Step 3
T hese are the properties of Rectangle, theref ore this shape is a Rectangle
(6) b. (-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 : us-9-Coordinate-Geometry [8]
(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. 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
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ID : us-9-Coordinate-Geometry [9]
(9) d. (-15, 40)
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 40. T heref ore, the y-coordinate of the
point is 40.
Step 4
Hence the coordinates of the given point are (-15, 40).
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ID : us-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.
(11) 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 : us-9-Coordinate-Geometry [11]
(12) a. T hird 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 negative, and the second is negative, so it lies in the T hird
quadrant.
(13) c. (0,6)
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 y-axis, then the abscissa value is
0.
Here we are given the ordinate value, and told that the point lies on the y axis, so the
answer is (0,6)
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ID : us-9-Coordinate-Geometry [12]
(14) b. -50
From observation we see that the point def ined is (30,-35)
We are told that
30 = p + 80, and
-35 = p + 15
From either of these equations we can see that p = -50
(15) 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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