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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

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

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 5.
The distance of the point (α, β) from origin is
a. α.β
b. α2. β2
c. \(\sqrt{\alpha^{2}-\beta^{2}}\)
d. \(\sqrt{\alpha^{2}+\beta^{2}}\)
Answer:
d. \(\sqrt{\alpha^{2}+\beta^{2}}\)

Question 6.
The distance between the point (x1,y1) and (x2, y2) is
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 1
Answer:
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 2

Question 7.
Which of the following is distance formula?
Answer:
a. The distance between 2 points (x1,y1) and (x2, y2) is
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 3

b. The mid point of the lines segment join the points (x, y) and (x2, y2)
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 4

c. The co-ordinates of the centroid of the ∆le ABC where A, B, C are (x1,y1)
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 5

d.
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 6

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

Question 8.
The distance b/w the point (0, 3) and (- 2, 0) is
a. \(\sqrt{14}\)
b. \(\sqrt{15}\)
c. \(\sqrt{13}\)
d. \(\sqrt{5}\)
Answer:
c. \(\sqrt{13}\)

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
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 7
Answer:
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 8

Question 11.
If the distance b/w the point (3, a) and (4,1) is \(\sqrt{10}\), 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

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

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. \(\sqrt{2}\)
b. 2
c. \(\sqrt{3}\)
d. 1
Answer:
a. \(\sqrt{2}\)

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 4.
Find the distance of B(3 + \(\sqrt{3}\), 3 – \(\sqrt{3}\)) form origin.
Answer:
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 9
d = \(\sqrt{24}\)
d = \(\sqrt{4 \times 6}\)
d = 2\(\sqrt{6}\)

Question 5.
Write the formula to find distance b/w two points
Answer:
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 10

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

Question 6.
Write the formula to find distance b/W point and origin.
Answer:
d = \(\sqrt{x^{2}+y^{2}}\)

Question 7.
Write the formula to find area of triangle.
Answer:
area of triangle
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 11

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
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 12

III. Long Answer Questions:

Question 1.
Find the distance between the following pairs of points.
i) (6, 5) and (4, 4)
Answer:
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 13
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 14

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

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
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 15
(∵ 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.
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 16
6y – 4y = 25 – 29
2y = – 4
y = \(\frac{-4}{2}\) ⇒ 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)
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 17

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:
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 18
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 19
∴ AD = BC & AB = CD
∴ Given vertices from a parallelogram.

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

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)
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 20
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 20
4m – 3n = – 2(m + n)
4m – 3n = – 2m – 2n
4m + 2m = – 2n + 3n
6m = n
\(\frac{m}{n}=\frac{1}{6}\)
m : n = 1 : 6 (or)
\(\frac{-9 m+5 n}{m+n}\) = 3
– 9m + 5n = 3(m + n)
– 9m + 5n = 3m + 3n
– 9m – 3m = 3n – 5n
– 12m = – 2n
\(\frac{m}{n}=\frac{-2}{-12}=\frac{1}{6}\)
m : n = 1 : 6

Question 7.
In the point C(1, 1) divides the line segment joining A(- 2, 7) and B in the ration 3 : 2 find the co-ordinates of B.
Answer:
Point C(1, 1)
(x1, y1) = A(- 2, 7) m : n = 3 : 2
B(x2, y2) =?

KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 22
∴ Co-ordinate of B = (3, – 3)

Question 8.
Find the ratio in which the point (- 1, k) divides the line joining the points (- 3, 10) and (6, – 8) and also find ‘k’.
Answer:
P(x, y) = (- 1, k); (x1, y1) = (- 3,10)
(x2, y2) = (6,- 8)
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 23
6m – 3n = – (m + n)
6m – 3n = – m – n
6m + m = 3n – n, \(\frac{-8 m+10 n}{m+n}\) = k
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 24

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

Question 9.
Three Consecutive vertices of a parallelogram are A(1, 2), B(2, 3) and (8, 5). Find the fourth vertex.
Answer:
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 25
‘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
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 26
Co-ordinates of ‘O’ = \(\frac{9}{2}, \frac{7}{2}\)
BD is a line and ‘O’ is midpoint
B(2, 3) = (x1, y1); D(x, y) = (x2, y2)
\(\left(\frac{9}{2} \frac{7}{2}\right)\) = (x, y)
By midpoint formula
Co-ordinates of
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 27
2 + x = 9 3 + y = 7
x = 9 – 2 y = 7 – 3
x = 7 y = 4
the fourth vertex is (7, 4)

Question 10.
Find the relation between x and y, if the points (x, y) (1, 2) and (7, 0) are colliner.
Answer:
Given point are A(x, y), B(1, 2) and C(7, 0)
These points will be collinear if the area of the triangle formed by them is zero.
Now, ar(ABC)
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 28
⇒ 2x + 6y – 14 = 0
⇒ x + 3y = 7
which is the required relation between x & y

Question 11.
Find the ratio in which the line segment joining the points A(3, – 3) and B(- 2,7) is divides by x-axis. Also find the Co-ordinates of the point of division.
Answer:
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 29
Here, point Q is an x-axis its ordinate & 0
Let ratio be k : 1 and Co-ordinate of point Q be (x, 0)
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 30

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

Question 12.
If A(4, 2), B = (7, 6) and C(1, 4) are the vertices of ∆ ABC and AD is its median, P.T that median AD divides ∆ ABC into two triangle of equal areas.D is the median on BC
⇒ The Co-ordinates of midpoint D are given by
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 31
Co-ordinates of D are (4, 5)
Now, Area of triangle
ABD = \(\frac{1}{2}\)[x1 (y2 – y3) + x2 (y3 – y1) + x3 (y1 – y2)
= \(\frac{1}{2}\)[4(6 – 5) + 7(52) + 4(2 – 6)
= \(\frac{1}{2}\)[4 + 21 – 16] = \(\frac{1}{2}\) sq.units
Area of
∆ ACD = \(\frac{1}{2}\)[4[4 – 5] + 1[5 – 2] + 4[2 – 4]]
= \(\frac{1}{2}\)[- 4 + 3 – 8] = \(\frac{-9}{2}=\frac{9}{2}\) sq.units

Question 13.
In what ratio does the y – axis divide the line segment joining the point p(- 4, 5) and Q(3, 7). Also, find the co-ordinates of the intersection.
Answer:
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 32
Suppose y – axis divides PQ in the ratio k : 1. Then the co-ordinates of the point of division are
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 33
Since, R lies on y-axis and X Co-ordinate of every point on y-axis is zero.
∴ \(\frac{3 \mathrm{K}-4}{\mathrm{K}+1}\) = 0
⇒ 3k – 4 = 0 ⇒ K = \(\frac{4}{3}\)
Hence, the required ratio is 4/3 : 1 i.e, 4 : 3
Putting K = 4/3 in the Co-ordinates of R, we find that its Co-ordinates are (0, – 13/7)

Question 14.
Show that ∆ ABC with vertices A(- 2, 0), B(2, 0) and C(0, 2) is similar to ∆ DEF with vertices D(- 4, 0), E(4, 0) and F(0, 4)
Answer:
Given vertices of ∆ ABC and ∆ DEF are
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 34
A(- 2, 0), B(2, 0), C(0, 2), D(- 4, 0), E(4, 0) and F(0, 4)
KSEEB Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Additional Questions 35
Here, we see that sides of ∆ DEF are twice the sides of a ∆ ABC.
Hence, both triangle are similar.

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

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