Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev

The document Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
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Q.1. Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3.
Sol. Let P(x, y) be the point.
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
y = 3
Then, the coordinates of point are (1,3)

Q.2. Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).
Sol.  Let points P and Q trisect the line joining the points.
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
∴ AP = PQ = QB
P divides AB in the ratio 1:2 and Q divides AB in the ratio 2:1
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev

Q.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 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?
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Sol. 
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Coordinates of green flag are P(2, 25)
The coordinates of red flag are Q(8, 20)
The distance between two points is
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Position of the blue flag = mid-point of PQ
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
∴ The blue flag is in the 5th line, at a distance of 22.5 m.

Q.4. Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).
Sol. Let the required ratio be k : 1
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
∴ The required ratio is 2:7.

Q.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.
Sol. Let P(x, 0) divide the line segment AB in the ratio k : 1
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
0 = 5k - 5 ⇒ 5k = 5 k = 1
Hence the required ratio is 1 : 1, at point Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev

Q.6. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Sol. 
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Mid-point of AC = Mid-point of BD
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev

Q.7. 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).
Sol. Let the coordinates of A be (x, y). O (2, - 3) is the mid-point of AB
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
⇒ x + 1 = 4, ⇒ y + 4 = -6
⇒ x = 4 - 1, ⇒ y = -6 - 4
⇒ x = 3, ⇒ y = -10
Hence, the coordinates of A are (3, -10).

Q.8. If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev and P lies on the line segment AB.
Sol.
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Hence, the coordinates of P are Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev

Q.9. Find the coordinates of the points which divide the line segment joining A (-2, 2) and B (2, 8) into four equal parts.
Sol. P, Q, R divide AB into four equal parts
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Now, Q is the mid-point of AB.
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
P is the mid-point of AQ, then the coordinates of P are
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
R is the mid-point of QB, the coordinates of R are
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev

Q.10. 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)]
Sol. Let points be A (3,0), B(4, 5), C(-1, 4) and D(-2, -1)
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev
Ex 7.2 NCERT Solutions- Coordinate Geometry Class 10 Notes | EduRev

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