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**NCERT Class 10 Mathematics Chapter 7 Coordinate Geometry**

**NCERT Class 10 Mathematics Chapter 7 Coordinate Geometry**Also, you can read the CBSE book online in these sections Solutions by Expert Teachers as per (CBSE) Book guidelines. **NCERT****Class 10 Mathematics Textual Question Answer. **These solutions are part of NCERT All Subject Solutions. Here we have given

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**Solutions****NCERT Class 10 Mathematics Chapter 7 Coordinate Geometry****Coordinate Geometry**

**Coordinate Geometry****Chapter – 7**

Exercise 7.1 |

**1. Find the distance between the following pairs of points:**

**(i) (2, 3), (4, 1)**

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**(ii) (−5, 7), (−1, 3)**

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**(iii) (a, b), (− a, − b)**

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**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.**

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Yes, we can find the distance between the given towns A and B. Assume town A at origin point (0, 0). Therefore, town B will be at point (36, 15) with respect to town A. And hence, as calculated above, the distance between town A and B will be 39 km.

**3. Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.**

Ans: Let the points (1, 5), (2, 3), and (−2, −11) be representing the vertices A, B, and C of the given triangle respectively.

Therefore, the points (1, 5), (2, 3), and (−2, −11) are not collinear.

**4. Check whether (5, − 2), (6, 4) and (7, − 2) are the vertices of an isosceles triangle.**

Ans: Let the points (5, −2), (6, 4), and (7, −2) are representing the vertices A, B, and C of the given triangle respectively.

As two sides are equal in length, therefore ABC is an isosceles triangle

**5. In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following 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. **

Ans: It can be observed that A (3, 4), B (6, 7), C (9, 4), and D (6, 1) are the positions of these 4 friends.

It can be observed that all sides of this quadrilateral ABCD are of the same length and also the diagonals are of the same length. Therefore, ABCD is a square and hence, Champa was correct.

**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)**

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**(ii) Let the points (− 3, 5), (3, 1), (0, 3), and (−1, −4) be representing the vertices A, B, C, and D of the given quadrilateral respectively. **

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**(iii) Let the points (4, 5), (7, 6), (4, 3), and (1, 2) be representing the vertices A, B, C, and D of the given quadrilateral respectively.**

Ans: Let the points (4, 5), (7, 6), (4, 3), and (1, 2) be representing the vertices A, B, C, and D of the given quadrilateral respectively.

It can be observed that opposite sides of this quadrilateral are of the same length. However, the diagonals are of different lengths. Therefore, the given points are the vertices of a parallelogram.

**7. Find the point on the x-axis which is equidistant from (2, − 5) and (− 2, 9).**

Ans: We have to find a point on x-axis. Therefore, its y-coordinate will be 0.

By the given condition, these distances are equal in measure

**8. Find the values of y for which the distance between the points P (2, − 3) and Q (10, y) is 10 units.**

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**9. If Q (0, 1) is equidistant from P (5, − 3) and R (x, 6), find the values of x. Also find the distance QR and PR.**

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**10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (− 3, 4). **

Ans: Point (x, y) is equidistant from (3, 6) and (−3, 4).

Exercise 7.2 |

**1. Find the coordinates of the point which divides the join of (− 1, 7) and (4, − 3) in the ratio 2:3.**

Ans: Let P(x, y) be the required point. Using the section formula, we obtain (− 2, − 3).

Let P (x1, y1) and Q (x2, y2) are the points of trisection of the line segment joining the given points i.e., AP = PQ = QB Therefore, point P divides AB internally in the ratio 1:2.

**3. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the following figure. Niharika runs 1 4 𝑡ℎ the distance AD on the 2nd line and posts a green flag. Preet runs 1 5 𝑡ℎ the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?**

Ans: It can be observed that Niharika posted the green flag at 1/4 of the distance AD i.e.,

**4. Find the ratio in which the line segment joining the points (− 3, 10) and (6, − 8) is divided by (− 1, 6).**

Ans: Let the ratio in which the line segment joining (−3, 10) and (6, −8) is divided by point (−1, 6) be k:1.

**5. Find the ratio in which the line segment joining A (1, − 5) and B (− 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.**

Ans: Let the ratio in which the line segment joining A (1, −5) and B (−4, 5) is divided by x – axis be k:1

x – axis be k:1

**6. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.**

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Let (1, 2), (4, y), (x, 6), and (3, 5) are the coordinates of A, B, C, D vertices of a parallelogram ABCD. Intersection point O of diagonal AC and BD also divides these diagonals. Therefore, O is the midpoint of AC and BD. If O is the midpoint of AC, then the coordinates of O are

**7. Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, − 3) and B is (1, 4)**

Ans: Let the coordinates of point A be (x, y).

Midpoint of AB is (2, −3), which is the center of the circle.

**8. If A and B are (− 2, − 2) and (2, − 4), respectively, find the coordinates of P such that 𝐴𝑃 = 3 7 𝐴𝐵 and P lies on the line segment AB.**

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**9. Find the coordinates of the points which divide the line segment joining A (− 2, 2) and B (2, 8) into four equal parts.**

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**10. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (− 1, 4) and (− 2, −1) taken in order.**

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