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NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Q1. Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3.
Ans: Given,
Let P(x, y) be the required point.
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)Let A(−1, 7) and B(4, −3)
m: n = 2:3
Hence
x1 = −1
y1 = 7
x2 = 4
y2 = −3
By Section formula

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

By substituting the values in the Equation (1)
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Therefore, the co-ordinates of point P are (1, 3).

Q2. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).
Ans:  NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Given,
Let line segment joining the points be A(4, −1) and B(−2, −3).
Let P (x1, y1) and Q (x2, y2) be the points of trisection of the line segment joining the given points i.e., AP = PQ = QB
By Section formula
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Therefore, by observation point P divides AB internally in the ratio 1:2.
Hence m: n = 1:2
By substituting the values in the Equation (1)
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Therefore,NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Therefore, by observation point Q divides AB internally in the ratio 2:1.
Hence m:n = 2:1
By substituting the values in the Equation (1)
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Therefore, NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Hence the points of trisection are P(x1, y1) = NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)


Q3. 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 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?NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)Ans: From the Figure,
Given,

  • By observation, that Niharika posted the green flag at of the distance P i.e., NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)from the starting point of 2nd line. Therefore, the coordinates of this point P is (2, 25).
  • Similarly, Preet posted red flag at 1/5 of the distance NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)from the starting point of 8th line. Therefore, the coordinates of this point Q are (8, 20)

We know that the distance between the two points is given by the Distance Formula,
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

To find the distance between these flags PQ by substituting the values in Equation (1),
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

  • The point at which Rashmi should post her blue flag is the mid-point of the line joining these points. 
  • Let this point be M (x, y).

By Section formula
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Therefore, Rashmi should post her blue flag at 22.5 m on 5th line

Q4. Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Ans: From the figure,
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)Given, 

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

By Section formulaNCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Therefore,
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Hence the point P divides AB in the ratio 2:7


Q5. 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: From the Figure,NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)Given, 

  • Let the ratio be k : 1. 
  • Let the line segment joining A (1, −5) and B (−4, 5)

By Section formula
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
By substituting the values in Equation (1)
Therefore, the coordinates of the point of division is NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
We know that y-coordinate of any point on x-axis is 0.

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Therefore, x-axis divides it in the ratio 1:1.

Division point
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Q6. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Ans: From the Figure,NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Given, 

  • Let A (1, 2), B (4, y), C(x, 6), and D (3, 5) are the vertices of a parallelogram ABCD.
  • Since the diagonals of a parallelogram bisect each other, Intersection point O of diagonal AC and BD also divides these diagonals

Therefore, O is the mid-point of AC and BD.
If O is the mid-point of AC, then the coordinates of O are

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
If O is the mid-point of BD, then the coordinates of O are

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Since both the coordinates are of the same point O,
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Q7. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).
Ans: From the Figure,
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Given, 

  • Let the coordinates of point A be (x, y). 
  • Mid-point of AB is C (2, −3), which is the center of the circle.

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Therefore, the coordinates of A are (3, −10)

Q8. If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2) and P lies on the line segment AB.
Ans: From the Figure,
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)Given,

  • The coordinates of point A and B are (−2, −2) and (2, −4) respectively.
  • AP = 3/7AB

Hence AB/AP = 7/3
We know that AB = AP + PB from figure,
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Therefore, AP:PB = 3:4
Point P(x, y) divides the line segment AB in the ratio 3:4. Using Section Formula,

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Q9. Find the coordinates of the points which divide the line segment joining A (-2, 2) and B (2, 8) into four equal parts.
Ans: From the Figure,
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

By observation, that points P, Q, R divides the line segment A (−2, 2) and B (2, 8) into four equal parts
Point P divides the line segment AQ into two equal parts
Hence, Coordinates of P = NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
= NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Point Q divides the line segment AB into two equal parts
Coordinates of Q
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Point R divides the line segment BQ into two equal parts
Coordinates of R
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)



Q10. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order. [Hint: Area of a rhombus = 1/2 (product of its diagonals)]
Ans: From the Figure,

NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)Given, 

  • Let A(3, 0), B(4, 5), C(−1, 4) and D(−2, −1) are the vertices of a rhombus ABCD.

We know that the distance between the two points is given by the Distance Formula,
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)Therefore, distance between A (3, 0) and C (−1, 4) is given by
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

Therefore, distance between B (4, 5) and D (−2, −1) is given by
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
Area of the rhombus ABCD  = 1/2 x (Product of lengths of diagonals)
= 1/2 AC x BD
Therefore, area of rhombus
NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)
= 24 Square units

The document NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2) is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on NCERT Solutions for Class 10 Maths Chapter 7 - Coordinate Geometry (Exercise 7.2)

1. What are the basic concepts of coordinate geometry?
Ans. Coordinate geometry deals with the study of geometric shapes using coordinate systems. It involves points, lines, curves, and shapes represented by coordinates on a graph.
2. How do you find the distance between two points in coordinate geometry?
Ans. The distance between two points (x1, y1) and (x2, y2) in coordinate geometry can be calculated using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2).
3. What is the slope of a line in coordinate geometry?
Ans. The slope of a line in coordinate geometry represents the rate of change in the vertical direction compared to the horizontal direction. It is calculated as the ratio of the difference in y-coordinates to the difference in x-coordinates.
4. How do you find the midpoint of a line segment in coordinate geometry?
Ans. The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found by taking the average of the x-coordinates and y-coordinates: ((x1 + x2)/2, (y1 + y2)/2).
5. Can you explain the concept of parallel and perpendicular lines in coordinate geometry?
Ans. In coordinate geometry, two lines are parallel if they have the same slope, and they will never intersect. Two lines are perpendicular if the product of their slopes is -1, indicating that they intersect at a right angle.
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