1.Coordinate Plane in Class 9

Coordinate Plane in Class 9

Do you know coordinate plane in Class 9?In this article we will read coordinate plane Questions with Solution.
“Before moving to Part 2,read our basic introduction to The Use of Coordinates Class 9.”

2.Important Points of Coordinate Plane in Class 9

(1.)To locate the position of an object or a point in a plane, we require two perpendicular lines-One of them is horizontal, and the other is vertical.
(2.)The plane is called the cartesian plane, the coordinate plane or the xy-plane and the lines are called the coordinate axes.
(3.)The horizontal line is called the x-axis and the vertical line is called the y-axis.
(4.)The coordinate axes divide the plane into four parts called quadrants.
Using the conventions that we have stated earlier:
(5.)Points in Quadrant I have both x- and y-coordinates positive.
(6.)Points in Quadrant II have negative x-coordinate and positive y-coordinate.
(7.)Points in Quadrant III have both x- and y-coordinates negative.
(8.)Points in Quadrant IV have positive x-coordinate and negative y-coordinate.
(9.)The point of intersection of the axes is called the origin.
(10.)The distance of a point from the y-axis is its x-coordinate and the distance of the point from the x-axis is its y-coordinate.If the x-coordinate of a point is x, and the y-coordinate is y, then (x,y) are called the coordinates of the point.
(11.)The coordinates of a point on the x-axis are of the form (x,0) and those of the points on the y-axis are of the form (0,y)
(12.)The coordinates of the origin are (0,0).
(13.)The coordinates of a point are of the form (+,+) in the first quadrant, (-,+) in the second quadrant, (-,-) in the third quadrant and (+,-) in the fourth quadrant.If x=y then (x,y)=(y,x) If x=y, then (x,y)=(y,x)

3.Examples Based on Coordinate Plane in Class 9

So far,we have only considered points on the two coordinate axes.What can you say about the coordinates of points that are not on either axes? The plane in which the axes are situated is called the Cartesian plane, the coordinate plane or the xy-plane. The axes divide the plane into four parts, called quadrants.They are numbered as shown in Fig. 1.4

Coordinate Plane in Class 9

Example:1.Place Reiaan’s rectangular study table with three of its feet at the points (8, 9), (11, 9) and (11, 7).
(i) Where will the fourth foot of the table be?
Solution:A rectangle has opposite sides equal and parallel.
The x-coordinates for the right edge are both 11 (from (11, 9) and (11,7)).
The top edge has y-coordinates of 9 (from (8, 9) and (11, 9)).
Therefore,the fourth corner must share the x-coordinate of the left side (8) and the y-coordinate of the bottom side (7).
Answer: (8, 7)
Example1:(ii).Is this a good spot for the table?
Solution:Yes,placed against a wall or in the designated study corner on the grid,it leaves adequate movement space in the room without blocking pathways.
Example:(iii).What is the width of the table? The length? Can you make out the height of the table?
Solution:Width (Horizontal distance): Difference in x-coordinates=11-8=3 units or 3 ft
Length (Vertical distance):Difference in y-coordinates=9-7 = 2 units or 2 ft}
Can you make out the height?
Answer:No.A coordinate plane (2D graph) only shows the x (length/width) and y (length/width) dimensions.Height requires a z-axis (3D geometry).
Example:2.If the bathroom door has a hinge at B_1,and opens into the bedroom,will it hit the wardrobe? Are there any changes you would suggest if the door is made wider?
Answer:No,provided the door’s swing radius (arc length) is less than the clearance distance between point B_1 and the wardrobe edge.
Suggestions if the door is made wider:If widened,the door’s swing arc will increase and may hit the wardrobe or block access.To fix this,suggest changing the hinge side or using a sliding door/ inward-folding door.
Example:3.Look at Reiaan’s bathroom.
(i) What are the coordinates of the four corners O,F,R and P of the bathroom?
Solution:O:(0,0) (Origin),F:(0,9),R: (-6,9),P:(-6,0)
Example:3(ii).What is the shape of the showering area SHWR in Reiaan’s bathroom? Write the coordinates of the four corners.
Solution:Shape:It forms a trapezium
Coordinates:S:(-6,6),H:(-3,6),W:(-2,9),R:(-6,9)
Example:3(iii).Mark off a 3 ft x 2 ft space for the washbasin and a 2 ft x 3 ft space for the toilet.Write the coordinates of the corners of these spaces.
Solution:Toilet(2 ft ×3 ft):Corners at (-6,3), (-5.5,3),(-6,4.5),(-6.5,4.5).
Washbasin (3 ft × 2 ft):Corners at (-6,0.5),(-5,0. 5),(-6,2),(-5,2).
Example:4.Other rooms in the house:
Example:4(i).Reiaan’s room door leads from the dining room which has the length 18 ft and width 15 ft. The length of the dining room extends from point P to point A.Sketch the dining room and mark the coordinates of its corners.
Solution:Length P to A=(12-(-6))=12+6=18
Width 15 ft=y-axis negative side i.e. below the diagram
Coordinates of Corner
P(-6,0),A(12,0),Bottom Right corner:(12,-25),Bottom Laft corner:(-6,-15)

Coordinate Plane in Class 9

Example:4(ii)Place a rectangular 5ft x 3 ft dining table precisely in the centre of the dining room.Write down the coordinates of the feet of the table.
Solution:Table (5 ft × 3 ft) precisely at the centre:
Center of Dining Room:
x-center=\frac{-6+12}{2}=3 ,y-center=\frac{0+(-15)}{2}=-7.5
Table Dimensions 5 ft × 3 ft
x-range:from 3-2.5=0.5 to 3+3.5=5.5
y-range:from -7.5-1.5=-9 to -7.5+1.5=-6
Coordinates of Table feet:
Foot 1: (0.5,-6)
Foot 2: (5.5,-6)
Foot 3: (5.5,-9)
Foot 4: (0.5,-9)
With the above illustrations,one can understand the Coordinate Plane in Class 9.

Also Read This Article:- Coordinate system

4.Practice Problems of Coordinate Plane in Class 9 for Students

Coordinate Plane in Class 9

(1.)Does point Q (y,x) ever coincide with point P (x,y)? Justify your answer
(2.)If x=y,then (x y)=(y,x); and (x,y)=(y,x) if and only if x=y. Is this claim true?
By solving the above questions,you can understand the Coordinate Plane in Class 9 well because the concept is well understood when you solve it practically.

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Also Read This Article:- Class 9 Rational and Irrational Number

5.Frequently Asked Questions Related to Coordinate Plane in Class 9

**छात्र-छात्राओं से आज का सवाल**

*”80 के ऐसे चार भाग करो कि उनमें 3 जोड़ें,तीन घटाएं,तीन का गुणा करें तथा 3 का भाग दें तो समान उत्तर प्राप्त हो।”*
**Today’s Question to Students**
*”Divide 80 into four such parts that add 3 to them,subtract three,multiply three and divide 3 to get the same answer.”*
*पिछली प्रश्नोत्तरी का उत्तर*
123+4-5+67-89=100
*Previous Quiz Solution*
123+4-5+67-89=100
*”This article has been prepared by **Satyam Coaching Centre** on the **Satyam Mathematics** blog.”*