BSEB Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 7 Coordinate Geometry Ex 7.1 Book Answers |
Bihar Board Class 10th Maths Chapter 7 Coordinate Geometry Ex 7.1 Textbooks Solutions PDF
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Board | BSEB |
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Format | DOC/PDF |
Class | 10th |
Subject | Maths Chapter 7 Coordinate Geometry Ex 7.1 |
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BSEB Class 10th Maths Chapter 7 Coordinate Geometry Ex 7.1 Textbooks Solutions with Answer PDF Download
Find below the list of all BSEB Class 10th Maths Chapter 7 Coordinate Geometry Ex 7.1 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:BSEB Bihar Board Class 10th Maths Solutions Chapter 7 Coordinate Geometry Ex 7.1
Question 1.
Find the distance between the following pairs of points :
(i) (2, 3), (4, 1)
(ii) (- 5, 7), (- 1, 3)
(iii) (a, b), (- a, – b)
Solution:
(i) Let P(2, 3) and Q(4, 1) be the given points.
Here, x1 = 2, y1 = 3 and x2 = 4, y2 = 1.
∴ PQ = (𝑥2−𝑥1)2+(𝑦2−𝑦1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
So, PQ = (4−2)2+(1−3)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ = (2)2+(−2)2‾‾‾‾‾‾‾‾‾‾‾‾√
or PQ = 4+4‾‾‾‾‾√ = 8‾√ = 22‾√
(ii) Let P(- 5, 7) and Q(- 1, 3) be the given points.
Here, x1 = -5, y1 = 7 and x2 = -1, y2 = 3.
∴ PQ = (𝑥2−𝑥1)2+(𝑦2−𝑦1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
So, PQ = (−1+5)2+(3−7)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ = (4)2+(−4)2‾‾‾‾‾‾‾‾‾‾‾‾√
or PQ = 16+16‾‾‾‾‾‾‾‾√ = 32‾‾‾√ = 16×2‾‾‾‾‾‾√ = 42‾√
(iii) Let P(a, b) and Q(- a, – b) be the given points.
Here, x1 = a, y1 = b and x2 = a, y2 = – b.
∴ PQ = (𝑥2−𝑥1)2+(𝑦2−𝑦1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
So, PQ = (−𝑎−𝑎)2+(−𝑏−𝑏)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
= (−2𝑎)2+(−2𝑏)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
or PQ = 4𝑎2+4𝑏2‾‾‾‾‾‾‾‾‾√
= 2𝑎2+𝑏2‾‾‾‾‾‾‾√
Question 2.
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2?
Solution:
Let P(0, 0) and Q(36, 15) be the given points.
Here, x1 = 0, y1 = 0 and x2 = 36, y2 = 15.
∴ PQ = (𝑥2−𝑥1)2+(𝑦2−𝑦1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
So, PQ = (36−0)2+(15−0)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ = 1296+225‾‾‾‾‾‾‾‾‾‾‾√
= 1521‾‾‾‾‾√ = 39
In fact, the positions of towns A and B are given by (0, 0) and (36, 15) respectively and so the distance between them = 39 km as calculated above.
Question 3.
Determine if the points (1, 5), (2, 3) and (- 2, – 11) are collinear.
Solution:
Let A(1, 5), B(2, 3) and C(- 2, – 11) be the given points. Then, we have :
Clearly, BC ≠ AB + AC, AB ≠ BC + AC and AC ≠ BC + AB.
Hence, A, B and C are not collinear.
Question 4.
Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Solution:
Let A(5, – 2), B(6, 4) and C(7, – 2) are the given points. Then,
AB = (6−5)2+(4+2)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
= 1+36‾‾‾‾‾‾√
= 37‾‾‾√
BC = (7−6)2+(−2−4)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
= 1+36‾‾‾‾‾‾√
= 37‾‾‾√
Clearly, AB = BC
∴ ∆ ABC is an isosceles triangle.
Question 5.
In a classroom, four friends are Seated at the points A, B, C and D as shown in figure. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square ?” Chameli disagrees. Using distance formula, find which of them is correct, and why?
Solution:
Clearly from the figure, the coordinates of points A, B, C and D are (3, 4), (6, 7), (9, 4) and (6, 1).
By using distance formula, we get
Thus, the four sides are equal and the diagonals are also equal. Therefore, ABCD is a square.
Hence, Champa is correct.
Question 6.
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer :
(i) (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0)
(ii) (-3, 5), (3, 1), (0, 3), (- 1,-4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Solution:
(i) Let A(- 1, – 2), B(1, 0), C(- 1, 2) and D(- 3, 0) be the given points. Then,
Clearly, four sides AB, BC, CD and DA are equal.
Also, diagonals AC and BD are equal.
∴ The quadrilateral ABCD is a square.
(ii) Let A(- 3, 5), B(3, 1), C(0. 3) and D(- 1, – 4) be the given points. Plot these points as shown.
Clearly, the points A, C and B are collinear.
So, no quadrilateral is formed by these points.
Aliter :
AB = (3+3)2+(1−5)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
= 36+16‾‾‾‾‾‾‾‾√
= 52‾‾‾√
= 213‾‾‾√
BC = (3−0)2+(1−3)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
and AC = (0+3)2+(3−5)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ = 13‾‾‾√
So, AC = AB + BC.
Hence, there, will not be any quadrilateral.
(iii) Let A(4, 5), B(7, 6), C(4, 3) and D(1, 2) be the .given points. Then,
Clearly, AB = CD, BC = DA and AC = BD.
∴ The quadrilateral ABCD is a parallelogram.
Question 7.
Find the point on the x-axis which is equidistant from (2, – 5) and (- 2, 9).
Solution:
Since the point on x-axis have its ordinate – 0, so P(x, 0) is any point on the x-axis.
Since P(x, 0) is equidistant from A(2, – 5) and P (- 2, 9), therefore PA = PB gives. PA² = PB²
or (x – 2)² + (0 + 5)² = (x + 2)² + (0 – 9)²
or x² – 4x + 4 + 25 = x² + 4x + 4 + 81
or – 4x – 4x = 81 – 25
– 8x = 56
or x = 56−8 = – 7
∴ The point equidistant from given points on the x-axis is (- 7, 0).
Question 8.
Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units.
Solution:
P(2, – 3) and Q(10, y) are given points such that PQ = 10 units.
Thus, the possible value of y is – 9 or 3.
Question 9.
If Q(0, 1) is equidistant from P(5, – 3) and R(x, 6), find the values of x. Also, find the distances QR and PR.
Solution:
Since the point Q(0, 1) is equidistant from P(5, – 3) and R(x, 6), therefore
QP = QR gives QP² – QR²
or (5 – 0)² + (- 3 – 1)² = (x – 0)² + (6 – 1)²
or 25 + 16 = x² + 25
or x² = 16 So, x = ± 4
Thus, R is (4, 6) or (- 4, 6).
Now, QR = Distance between Q(0, 1) and R(4, 6)
(4−0)2+(6−1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ = 16+25‾‾‾‾‾‾‾‾√ = 41‾‾‾√
Also, QR = Distance between Q(0, 1) and R(- 4, 6)
(−4−0)2+(6−1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ = 16+25‾‾‾‾‾‾‾‾√ = 41‾‾‾√
and PR = Distance between P(5, – 3) and R(4, 6)
(4−5)2+(6+3)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ = 1+81‾‾‾‾‾‾√ = 82‾‾‾√
and PR = Distance between P(5, – 3) and R(-4, 6)
(−4−5)2+(6+3)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ = 81+81‾‾‾‾‾‾‾‾√ = 92‾√
Question 10.
Find a relation between x and y such that the point Or, y) is equidistant from the points (3, 6) and (-3,4).
Solution:
Let the point P(x, y) be equidistant from the points A(3, 6) and B(- 3, 4).
i.e., PA = PB gives PA² = PB²
or (x – 3)² + (y – 6)² = (x + 3)² + (y – 4)²
or x²- 6x + 9 + y² – 12y + 36 = x²+ 6x + 9 + y² – 8y + 16
or 6x – 6x – 12y + 8y + 36 – 16 0
or – 12x – 4y + 20 = 0
or 3x + y – 5 = 0,
which is the required relation.
BSEB Textbook Solutions PDF for Class 10th
- BSEB Class 10 Textbook Solutions PDF: Download Bihar Board STD 10th Book Answers
- BSEB Class 10 Maths Textbook Solutions PDF: Download Bihar Board STD 10th Maths Book Answers
- BSEB Class 10 Maths Chapter 1 Real Numbers Ex 1.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 1 Real Numbers Ex 1.1 Book Answers
- BSEB Class 10 Maths Chapter 1 Real Numbers Ex 1.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 1 Real Numbers Ex 1.2 Book Answers
- BSEB Class 10 Maths Chapter 1 Real Numbers Ex 1.3 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 1 Real Numbers Ex 1.3 Book Answers
- BSEB Class 10 Maths Chapter 1 Real Numbers Ex 1.4 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 1 Real Numbers Ex 1.4 Book Answers
- BSEB Class 10 Maths Chapter 2 Polynomials Ex 2.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 2 Polynomials Ex 2.1 Book Answers
- BSEB Class 10 Maths Chapter 2 Polynomials Ex 2.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 2 Polynomials Ex 2.2 Book Answers
- BSEB Class 10 Maths Chapter 2 Polynomials Ex 2.3 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 2 Polynomials Ex 2.3 Book Answers
- BSEB Class 10 Maths Chapter 2 Polynomials Ex 2.4 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 2 Polynomials Ex 2.4 Book Answers
- BSEB Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.1 Book Answers
- BSEB Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.2 Book Answers
- BSEB Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3 Book Answers
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- BSEB Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.7 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.7 Book Answers
- BSEB Class 10 Maths Chapter 4 Quadratic Equations Ex 4.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 4 Quadratic Equations Ex 4.1 Book Answers
- BSEB Class 10 Maths Chapter 4 Quadratic Equations Ex 4.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 4 Quadratic Equations Ex 4.2 Book Answers
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- BSEB Class 10 Maths Chapter 4 Quadratic Equations Ex 4.4 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 4 Quadratic Equations Ex 4.4 Book Answers
- BSEB Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 5 Arithmetic Progressions Ex 5.1 Book Answers
- BSEB Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 5 Arithmetic Progressions Ex 5.2 Book Answers
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- BSEB Class 10 Maths Chapter 5 Arithmetic Progressions Ex 5.4 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 5 Arithmetic Progressions Ex 5.4 Book Answers
- BSEB Class 10 Maths Chapter 6 Triangles Ex 6.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 6 Triangles Ex 6.1 Book Answers
- BSEB Class 10 Maths Chapter 6 Triangles Ex 6.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 6 Triangles Ex 6.2 Book Answers
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- BSEB Class 10 Maths Chapter 6 Triangles Ex 6.4 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 6 Triangles Ex 6.4 Book Answers
- BSEB Class 10 Maths Chapter 6 Triangles Ex 6.5 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 6 Triangles Ex 6.5 Book Answers
- BSEB Class 10 Maths Chapter 6 Triangles Ex 6.6 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 6 Triangles Ex 6.6 Book Answers
- BSEB Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 7 Coordinate Geometry Ex 7.1 Book Answers
- BSEB Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 7 Coordinate Geometry Ex 7.2 Book Answers
- BSEB Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 7 Coordinate Geometry Ex 7.3 Book Answers
- BSEB Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 7 Coordinate Geometry Ex 7.4 Book Answers
- BSEB Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 8 Introduction to Trigonometry Ex 8.1 Book Answers
- BSEB Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 8 Introduction to Trigonometry Ex 8.2 Book Answers
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- BSEB Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 8 Introduction to Trigonometry Ex 8.4 Book Answers
- BSEB Class 10 Maths Chapter 9 Some Applications of Trigonometry Ex 9.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 9 Some Applications of Trigonometry Ex 9.1 Book Answers
- BSEB Class 10 Maths Chapter 10 Circles Ex 10.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 10 Circles Ex 10.1 Book Answers
- BSEB Class 10 Maths Chapter 10 Circles Ex 10.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 10 Circles Ex 10.2 Book Answers
- BSEB Class 10 Maths Chapter 11 Constructions Ex 11.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 11 Constructions Ex 11.1 Book Answers
- BSEB Class 10 Maths Chapter 11 Constructions Ex 11.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 11 Constructions Ex 11.2 Book Answers
- BSEB Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 12 Areas Related to Circles Ex 12.1 Book Answers
- BSEB Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 12 Areas Related to Circles Ex 12.2 Book Answers
- BSEB Class 10 Maths Chapter 12 Areas Related to Circles Ex 12.3 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 12 Areas Related to Circles Ex 12.3 Book Answers
- BSEB Class 10 Maths Chapter 13 Surface Areas and Volumes Ex 13.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 13 Surface Areas and Volumes Ex 13.1 Book Answers
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- BSEB Class 10 Maths Chapter 13 Surface Areas and Volumes Ex 13.5 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 13 Surface Areas and Volumes Ex 13.5 Book Answers
- BSEB Class 10 Maths Chapter 14 Statistics Ex 14.1 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 14 Statistics Ex 14.1 Book Answers
- BSEB Class 10 Maths Chapter 14 Statistics Ex 14.2 Textbook Solutions PDF: Download Bihar Board STD 10th Maths Chapter 14 Statistics Ex 14.2 Book Answers
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