Constructions and Coordinate Geometry are important chapters to cover from the class 9 maths syllabus. Belonging to the geometry section of mathematics, both the chapters are unique and contain two very essential and fundamental concepts of mathematics. The application of coordinate geometry and construction together will be a part of the syllabus of higher standards as well as entrance and competitive exams, hence, you must aim to have a strong hold over the class 9 constructions chapter. Through this blog we aim to present detailed notes for class 9 coordinate geometry as well as constructions.
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Geometrical constructions are the method of representing a geometrical figure by using two instruments, a non-graduated ruler or straight edge and a compass. Here in this chapter, you will learn about some basic constructions. By following the methods provided in the class 9 construction chapter, you will be able to construct a certain variety of triangles. Mentioned below are some basic construction examples, through which you will learn to construct the given figure.
Sample Constructions 1: For a given angle, construct the bisector.
Step 1: Considering the B as centre, draw an arc of any radius, using compass thus resulting rays BA and BC. Name the intersecting points D and E correspondingly.
Step 2: Now consider D and E as centre’s to draw arcs such that both intersect each other at F point with a radius more than ½ of DE.
Step 3: At last, draw ray BF that is the required bisector for the ABC angle.
Sample Constructions 2: The next important question in our class 9 constructions chapter is, How to construct the perpendicular bisector for any given line segment.
Step 1: First take A and B as centre’s and draw arcs using a compass on both the sides of line segment AB that intersects each other with a radius more than ½ AB.
Step 2: Consider P and Q be the points where arcs intersect. And draw a line to join PQ.
Step 3: Consider M to be the point where AB and PQ line segment intersects. Results, PMQ is the perpendicular bisector of AB.
Sample Constructions 3: Derived from the class 9 constructions chapter, the next question is- For a given ray, how to construct a 60ᵒ angle of at the initial point.
Step 1: First, take A as centre; draw an arc using a compass with any radius. Name D is the intersecting point of AB.
Step 2: Consider the D as the centre and with the same radius as in step 1, draw again an arc and name point E at the intersection.
Step 3: At last, draw a ray called AC to pass through E. Then ∠ CAB is the resulting angle of 60°.
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Class 9 Coordinate Geometry
In the class 9 Coordinate Geometry topic you will learn how to identify a point in a space or plane. Learning of a point in space, called it as 3D Geometry whereas the same concepts in-plane is called Coordinate Geometry. Here are some important terms and definitions from the class 9 coordinate geometry.
Number Line: The below figure shows the number line, the numbers are marked negative in one direction and positive in the other direction from a fixed point called 0.
Origin: The reference point where distances are marked both in a positive and negative direction. From the figure, 0 represents the origin.
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Cartesian System: The method of fixing a point using vertical and horizontal lines.
(i) The above figure illustrates a Cartesian system drawn by combining horizontal and vertical lines.
(ii) The X’X horizontal line called the x-axis and YY’ vertical line called the y-axis.
(iii) Origin: The point where both X’X and Y’Y intersect each other and is denoted by O.
(iv) Now the axes separate the plane into four parts called “Quadrants”.
Some important pointers of class 9 coordinate geometry and class 9 constriction are-
- If a point lies in the 1st quadrant, then the point will form (+, +) because the 1st quadrant is with the positive x-axis and the positive y-axis.
- If a point lies in the 2nd quadrant, then the point will form (–, +) because the 2nd quadrant is with the negative x-axis and the positive y-axis
- If a point lies in the 3rd quadrant, then the point will form (–, –) because the 3rd quadrant is with the negative x-axis and the negative y-axis
- If a point lies in the 4th quadrant, then the point will form (+, –) because the 4th quadrant is with the positive x-axis and the negative y-axis
- The resulting plane is called a Cartesian plane and the axes are called coordinate axes
Coordinates of a Point
From the figure shown above, the point A is obtained after moving 2 units on the x-axis and 3 units on the y-axis.
- The +2 of point A represents X-coordinate and is called abscissa
- From the figure +3 of point A represents Y-coordinate and called as ordinate.
- The coordinates in the brackets show that the x-coordinate comes first, followed by the y-coordinate. Therefore (2, 3) are the coordinates of point A.
Construction Class 9 Explanation
Construction Class 9 Worksheet
Constructions Class 9 Extra Questions
- Draw a line segment AB = 8 cm. Draw ⅓ part of it. Measure the length of ⅓ part of AB.
- Why we cannot construct a ∆ABC, if ∠A = 60°, AB = 6 cm and AC + BC = 5 cm but construction of ∆ABC is possible if ∠A = 60°, AB = 6 cm and AC – BC = 5 cm ?
- Construct an angle of 90° at the initial point of the given ray.
- Draw a straight angle. Using compass bisect it. Name the angles obtained.
- Draw any reflex angle. Bisect it using a compass. Name the angles so obtained.
Constructions Class 9 MCQ
If a, b and c are the lengths of the three sides of a triangle, then which of the following is true?
(a) a + b < c
(b) a – b < c
(c) a + b = c
With the help of a ruler and compasses, which of the following is not possible to construct?
Which of the following angles can be constructed using ruler and compasses?
If the construction of a triangle ABC in which AB = 6 cm, ∠A = 70° and ∠B = 40° is possible then find the measure of ∠c.
The construction of a triangle ΔABC in which BC = 6 cm, ∠A = 50° is not possible when difference of BC and AC is equal to
(a) 4.6 cm
(b) 6.4 cm
(c) 5.1 cm
Thus, we hope that after going through these solved examples of class 9 constructions and class 9 coordinate geometry, you are now familiar with an interesting topic of mathematics. Reach out to our experts at Leverage Edu and they will help you draft a clear picture of your dream career.