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.
Let A(−1, 7) and B(4, −3)
m: n = 2:3
Hence
x_{1} = −1
y_{1} = 7
x_{2} = 4
y_{2} = −3
By Section formula
By substituting the values in the Equation (1)
Therefore, the coordinates 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:
Given,
Let line segment joining the points be A(4, −1) and B(−2, −3).
Let P (x_{1}, y_{1}) and Q (x_{2}, y_{2}) be the points of trisection of the line segment joining the given points i.e., AP = PQ = QB
By Section formula
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)
Therefore,
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)
Therefore,
Hence the points of trisection are P(x_{1}, y_{1}) =
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?Ans: From the Figure,
Given,
We know that the distance between the two points is given by the Distance Formula,
To find the distance between these flags PQ by substituting the values in Equation (1),
By Section formula
Therefore, Rashmi should post her blue flag at 22.5 m on 5^{th} 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,
Given,
By Section formula
Therefore,
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 xaxis. Also find the coordinates of the point of division.
Ans: From the Figure,Given,
By Section formula
By substituting the values in Equation (1)
Therefore, the coordinates of the point of division is
We know that ycoordinate of any point on xaxis is 0.
Therefore, xaxis divides it in the ratio 1:1.
Division point
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,
Given,
Therefore, O is the midpoint of AC and BD.
If O is the midpoint of AC, then the coordinates of O are
If O is the midpoint of BD, then the coordinates of O are
Since both the coordinates are of the same point O,
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,
Given,
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 and P lies on the line segment AB.
Ans: From the Figure,
Given,
Hence AB/AP = 7/3
We know that AB = AP + PB from figure,
Therefore, AP:PB = 3:4
Point P(x, y) divides the line segment AB in the ratio 3:4. Using Section Formula,
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,
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 =
=
Point Q divides the line segment AB into two equal parts
Coordinates of Q
Point R divides the line segment BQ into two equal parts
Coordinates of R
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,
Given,
We know that the distance between the two points is given by the Distance Formula,
Therefore, distance between A (3, 0) and C (−1, 4) is given by
Therefore, distance between B (4, 5) and D (−2, −1) is given by
Area of the rhombus ABCD = 1/2 x (Product of lengths of diagonals)
= 1/2 AC x BD
Therefore, area of rhombus
= 24 Square units
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1. What are the basic concepts of coordinate geometry? 
2. How do you find the distance between two points in coordinate geometry? 
3. What is the slope of a line in coordinate geometry? 
4. How do you find the midpoint of a line segment in coordinate geometry? 
5. Can you explain the concept of parallel and perpendicular lines in coordinate geometry? 

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