KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions

KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions

Karnataka State Syllabus Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions

I. Multiple-choice Questions:

Question 1.
The co-ordinates of origin are
a. 0,0.
b. 0, 1.
c. 1, 0.
d. 1, 1.
Answer:
a. 0,0.

Question 2.
The distance of the point (3, 4) x – co-ordinate is equal to
a. 3
b. 4
c. 1
d. 7
Answer:
b. 4

 

Question 3.
The distance of the point (3, 4) from y-axis is
a. 3
b. 4
c. 5
d. 1
Answer:
a. 3

Question 4.
The angle between x-axis and y-axis is
a. 0°
b. 45°
c. 60°
d. 90°
Answer:
d. 90°

Question 7.
Which of the following is distance formula?
Answer:
a. The distance between 2 points (x₁,y₁) and (x₂, y₂) is

b. The mid point of the lines segment join the points (x, y) and (x₂, y₂)

c. The co-ordinates of the centroid of the ∆^le ABC where A, B, C are (x₁,y₁)

d.

Question 9.
The ∆^le with vertices (- 2, 1) (2, – 2) and (5, 2) is
a. Scalene
b. Equilateral
c. Isosceles
d. right angled isosceles
Answer:
d. right angled isosceles

Question 10.
The Co-ordinates of the point which divides the join of (x, y) and (x₂, y₂) in the ratio m₁ : m₂ internally are

Answer:

Question 11.
If the distance b/w the point (3, a) and (4,1) is √10, then, find the values of a
a. 3,- 1
b. 4, – 2
c. 2, – 2
d. 5, – 3
Answer:
c. 2, – 2

Question 12.
The distance of the mid – point of the line -segment joining the points 6, 8. and 2, 4. from the point (1, 2) is
a. 3
b. 4
c. 5
d. 6
Answer:
c. 5

Question 13.
The coordinates of the mid – point of the line – segment joining (- 8, 13) and (x, – 7)
a. 16
b. 10
c. 4
d. 8
Answer:
a. 16

 

Question 14.
Find the value of k if the distance b/w (k, 3) and (2, 3) is 5
a. 5
b. 6
c. 7
d. 8
Answer:
c. 7

Question 15.
The distance b/w the point (Sin θ, Sin θ) & (cos θ, – cos θ) is
a. √2
b. 2
c. √3
d. 1
Answer:
a. √2

II. Short Answers Questions:

Question 1.
Write the coordinate of the origin.
Answer:
(0, 0)

Question 2.
What is the ordinate of all the point on x-axis
Answer:
0(zero)

Question 3.
Find the perpendicular distance of the point (- 3, 5) form the x – axis.
Answer:
5

Question 6.
Write the formula to find distance b/W point and origin.
Answer:
d = √x²+y²

Question 7.
Write the formula to find area of triangle.
Answer:
area of triangle

Question 8.
Find the value of a, so that the point (3, a) lie on the line 2x – 3y = 5.
Answer:
Since (3, a) lies on the line 2x – 3y = 5
Then 2(3) – 3(a) = 5
6 – 3a = 5
– 3a = 5 – 6
– 3a = – 1
a = 1/3

Question 9.
Write the section formula when it divide in ration p : q
Answer:
Co-ordinates

III. Long Answer Questions:

Question 1.
Find the distance between the following pairs of points.
i) (6, 5) and (4, 4)
Answer:

 

Question 2.
The distance between the point (3, 1) and (0, x) in 5 unit. Find x.
Answer:
(x₁, y₁) = (3, 1); (x₂, y₂) = (o, x)
d = 5

(∵ squaring on both the sides)
25 = (3)₂ + (x – 1)₂
x₂ + 1 – 2x + 9 = 25
x₂ + 1 – 2x + 9 – 25 = 0
x₂ + 1 – 2x + 9 – 25 = 0
x₂ – 2x – 15 = 0
x₂ – 5x + 3x – 15 = 0
x(x – 5) + 3(x – 5) = 0
(x – 5)(x + 3) = 0
x – 5 = 0, x + 3 = 0
x = 5, x = – 3

Question 3.
Find a point on y-axis which is equidistant from the points (5, 2) and (- 4, 3)
Answer:
A Point lie on y – axis = (0, y) the points are equidistant from the point on y – axis.

6y – 4y = 25 – 29
2y = – 4
y = −4/2 ⇒ y = – 2
∴ point on y – axis is y = – 2

Question 4.
Find the radius of a circle whose centre is (- 5, 4) and which passes through the point (- 7,1)

Question 5.
Prove that each of the set of co¬ordinates are the vertices of parallelograms.
i. (- 5, – 3), (1, – 11), (7, – 6), (1, 2).
Answer:

∴ AD = BC & AB = CD
∴ Given vertices from a parallelogram.

 

Question 6.
In what ratio does the point (- 2, 3) divide the line segment joining the point (- 3, 5) and (4, – a)?
Answer:
(x₁, y₁) = (3, 5)
(x₂, y₂) = (4, – a)
p(x, y) = (- 2, 3)

Question 9.
Three Consecutive vertices of a parallelogram are A(1, 2), B(2, 3) and (8, 5). Find the fourth vertex.
Answer:

‘O’ is the mid point of AC and by using mid point formulas AC is a line and ‘O’ is the point
A(x₁, y₁) =(1, 2);
c(x₂, y₂) = (8, 5)
Co-ordinates of

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