Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Previous Year Questions : Coordinate Geometry

Class 9 Maths - Coordinate Geometry Previous Year Questions

Very Short Answer Type Questions 

Q1. A line ∠M is drawn parallel to X-axis at a distance of 5 units from it. On ∠M a point P is marked at a distances of 3 units from the Y-axis. What are the coordinates of P?

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:

The line M can be above or below the x-axis

∴ coordinates of P are (3, 5) or (–3, 5)

Q2. Which of the following statements are true?

(i) The point (0, –4) lies on y-axis

(ii) The perpendicular distance of the point (5, 7) from the x-axis is 5.

(iii) Point (1, –1) and (–1, 1) lie in the same quadrant.

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol: Only the statement (i) is true.

 Q3. What is the sign of the y-coordinate of a point lying in the III-quadrant?

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol: The y-coordinate of a point in III-quadrant is always negative.

Q4. If the two points are A(–2, 7) and B(–3, 4) then what is (abscissa of A) – (abscissa of B)?

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol: ∵ abscissa of A = – 2 and abscissa of B = – 3
∵ (– 2) – (– 3) = –2 + 3 =1

Q5. A point (other than zero) is such that [The abscissa of the point] = [The ordinate of the point] In which quadrants can the point lie?

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol: ∵ The coordinates have opposite signs in II and IV quadrants.
∴ the given point lies in I or III quadrant.

Q6. A line ∠M is drawn parallel to X-axis at a distance of 5 units from it. On ∠M a point P is marked at a distances of 3 units from the Y-axis. What are the coordinates of P?

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol: The line M can be above or below the x-axis
∴ coordinates of P are (3, 5) or (–3, 5)

Short Answer Type Questions

Q1. Look at the following figure and answer the following:
(i) What is the abscissa of P?
(ii) What is the ordinate of Q?
(iii) What is the ordinate of R?
(iv) What is the abscissa of S?

Class 9 Maths - Coordinate Geometry Previous Year Questions

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol: (i) The abscissa of P is –3.
(ii) The ordinate of Q is –2.
(iii) The ordinate of R is 2.
(iv) The abscissa of S is –5.

Q2. Look at the following figure and answer the following:

Class 9 Maths - Coordinate Geometry Previous Year Questions

(i) Which point is having its ordinate as (–5)?
(ii) Which point is having abscissa as 4?
(iii) What are the coordinates of origin?
(iv) Which point is having abscissa as (–3)?

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol: (i) The point B is having its ordinate as (–5).
(ii) The point C is having its abscissa as 4.
(iii) The coordinates of O are (0, 0).
(iv) The point A is having abscissa as (–3).

Q3. Look at the following figure and answer the following:
(i) Which two points have the same abscissa?

(ii) Which two points have the same ordinate?

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol: 

(i) ∵ The abscissa of the point Q is 6.  
The abscissa of the point R is 6.
∴The points Q and R have the same abscissa.
(ii) ∵ The ordinate of P is (–3).  
The ordinate of R is (–3).
∴ The points P and R have the same ordinate.

Q4. Read the coordinates of the vertices of the triangle ABC in the following figure:

Class 9 Maths - Coordinate Geometry Previous Year Questions

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:

The vertices of the triangle are A, B and C.
The coordinates of A are (–6, 4).
The coordinates of B are (–3, –3).
The coordinates of C are (2, 2).

Q5. Write the coordinates of quadrilateral PQRS as shown in the following figure:

Class 9 Maths - Coordinate Geometry Previous Year Questions

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:

The vertices of the quadrilateral are P, Q, R and S.
The coordinates of P are (–4, 4).
The coordinates of Q are (8, 2).
The coordinates of R are (6, –3).
The coordinates of S are (–2, –2).

Long Answer Type Questions

Q1: If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex. (2011D)

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:

Let A (3,0), B (6, 0), C (x, y).

∴ ∆ABC is an equilateral

∴ AB = BC = AC

AB2 = BC2 = AC2 …[Squaring throughout

(6 – 3)2 + (0 – 0)2 = (x – 6)2 + (1 – 0)2 = (x – 3)2 + (y – 0)2

9 = x2 – 12x + 36 + y2 = x2 – 6x + 9 + y2

Class 9 Maths - Coordinate Geometry Previous Year Questions

Q2: If the vertices of a triangle are (1, -3), (4, p) and (-9, 7) and its area is 15 sq. units, find the value(s) of p.

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:

Area of ∆ = 15 sq. units

12 [1(p – 7) + 4(7 + 3)) + (-9)(-3 – p)] = ±15

p – 7 + 40 + 27 + 9p = ±30

10p + 60 = ± 30

10p = -60 ± 30

p = −60±30 / 10

∴ Taking +ve sign, p = −60 + 30 / 10 = −30 / 10 = -3

Taking -ve sign, p = −60 − 30 / 10 = −90 / 10 = -9

Q3: If A(4, 2), B(7,6) and C(1, 4) are the vertices of a AABC and AD is its median, prove that the median AD divides AABC into two triangles of equal areas.

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:

Class 9 Maths - Coordinate Geometry Previous Year Questions

Class 9 Maths - Coordinate Geometry Previous Year Questions

Area of ∆ABD

= 1/2 (x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]

= 1/2[4(6 – 5) + 7(5 – 2) + 4(2 – 6))

= 1/2(4 + 21 – 16) = 9/2 sq.units …(i)

Area of ∆ADC

= 1/2 [4(5 – 4) + 4(4 – 2) + 162 – 5)]

= 1/2(4 + 8 – 3) = 9/2sq.units

From (i) and (ii),

Area of ∆ABD = Area of ∆ADC

∴ Median AD divides ∆ABC into two triangles of equal area.

Q4: If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 square units, then prove that x + y = 15 or x + y = -9.

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:
Let A(x, y), B(1, 2), C(2, 1).
Area of ∆ABC = 6 sq. units …[Given
As 1/2 [x1(y2 – y3) + x2(y– y1) + x3(y1 – y2)] = 6
∴ x(2 – 1) + 1(1 – y) + 2(y – 2) = ±12
x + 1 – y + 2y – 4 = ±12
Taking +ve sign
x + y = 12 + 4 – 1
∴ x + y = 15
Taking -ve sign
x + y = -12 + 4 – 1
∴ x + y = -9

Q5: Point P(x, 4) lies on the line segment joining the points A(-5, 8) and B(4, -10). Find the ratio in which point P divides the line segment AB. Also find the value of x.

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:
Class 9 Maths - Coordinate Geometry Previous Year Questions

Q6: Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, -3). Also, find the value of x.

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:
Class 9 Maths - Coordinate Geometry Previous Year Questions

Q7: If P(2, 4) is equidistant from Q(7, 0) and R(x, 9), find the values of x. Also find the distance P.

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:
Class 9 Maths - Coordinate Geometry Previous Year QuestionsPQ = PR …[GivenPQ2 = PR2 … [Squaring both sides∴ (7 – 2)2 + (0 – 4)2 = (x – 2)2 + (9 – 4)2
⇒ 25 + 16 = (x – 2)2 + 25
⇒ 16 = (x – 2)2
⇒ ±4 = x – 2 …[Taking sq. root of both sides
⇒ 2 ± 4 = x
⇒ x = 2 + 4 = 6 or x = 2 – 4 = -2

Class 9 Maths - Coordinate Geometry Previous Year Questions

Q8: If the centroid of ∆ABC, in which A(a, b), B(b, c), C(c, a) is at the origin, then calculate the value of (a3 + b3 + c).

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:
Class 9 Maths - Coordinate Geometry Previous Year QuestionsCentroid = Class 9 Maths - Coordinate Geometry Previous Year Questions

Class 9 Maths - Coordinate Geometry Previous Year Questionsa + b + c = 0
If a + b + c = 0
then, as we know
a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b+ c2 – ab – bc – ac)
∴ a3 + b3 + c3 – 3abc = 0 … [Since a + b + c = 0
∴ a+ b3 + c3 = 3abc …(Hence proved)

Q9: Find the values of k so that the area of the triangle with vertices (k + 1, 1), (4, -3) and (7, -k) is 6 sq. units.

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:
Let A(k + 1, 1), B(4, -3) and C(7, -k).
We have, Area of ∆ABC = 6 … [Given
6 = 1/2 [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]
6 = 1/2[(k + 1)(-3 + k) + 4(-k – 1) + 7(1 + 3)]
12 = (-3k + k2 – 3 + k – 4k – 4 + 28]
12 = [k2 – 6k + 21]
⇒ k2 – 6k + 21 – 12 = 0
⇒ k2 – 6k + 9 = 0
⇒ k2 – 3k – 3k + 9 = 0
⇒ k(k – 3) – 3(k – 3) = 0 =
⇒ (k – 3) (k – 3) = 0
⇒ k – 3 = 0 or k – 3 = 0
⇒ k = 3 or k = 3
Solving to get k = 3.

Q10: For the triangle ABC formed by the points A(4, -6), B(3,-2) and C(5, 2), verify that median divides the triangle into two triangles of equal area.

Class 9 Maths - Coordinate Geometry Previous Year Questions  View Answer

Sol:
Let A(4, -6), B(3, -2) and C(5, 2) be the vertices of ∆ABC.
Since AD is the median
∴ D is the mid-point of BC.
⇒ D(3 + 5 / 2,−2 + 2 / 2) ⇒ D(4,0)
Area of ∆ABD
= 1/2 [4(-2 – 0) + 3(0 + 6) + 4(-6 + 2)]
= 1/2 [-8 + 18 – 16) = 1/2 [-6] = -3
But area of A cannot be negative.
∴ ar(∆ABD) = 3 sq.units …(i)
Area of ∆ADC
= 1/2 [4(0 – 2) + 4(2 + 6) + 5(-6 – 0)]
= 1/2(-8 + 32 – 30] = 12 [-6] = -3
But area of ∆ cannot be negative.
∴ ar(∆ADC) = 3 sq.units
From (i) and (ii),
∴ Median AD of AABC divides it into two ∆s of equal area.

The document Class 9 Maths - Coordinate Geometry Previous Year Questions is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Class 9 Maths - Coordinate Geometry Previous Year Questions

1. What are the basic concepts of coordinate geometry?
Ans. Coordinate geometry involves studying geometric figures using algebraic concepts. It includes points, lines, curves, and shapes on a coordinate plane using coordinates.
2. How is distance calculated in coordinate geometry?
Ans. The distance between two points in coordinate geometry is calculated using the distance formula, which is derived from the Pythagorean theorem.
3. What is the equation of a line in coordinate geometry?
Ans. The equation of a line in coordinate geometry is typically represented in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
4. How do we find the midpoint of a line segment in coordinate geometry?
Ans. The midpoint of a line segment in coordinate geometry can be found by averaging the x-coordinates and y-coordinates of the endpoints of the line segment.
5. What are the applications of coordinate geometry in real life?
Ans. Coordinate geometry is used in various fields such as engineering, architecture, navigation, and computer graphics for designing and analyzing geometric shapes and structures.
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