Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

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Class 10 : Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

The document Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev is a part of the Class 10 Course Class 10 Mathematics by VP Classes.
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Q21. Show that the triangle PQR formed by the points Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev and is an equilateral triangle. 

OR

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev 

Name the type of triangle PQR formed by the points  Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev and  Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q22. The line joining the points (2, − 1) and (5, − 6) is bisected at P. If P lies on the line 2x + 4y + k = 0, find the value of k.

 

Sol. We have A (2, − 1) and B (5, − 6).
∵ P is the mid point of AB,
∴ Coordinates of P are:

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Since P lies on the line 2x + 4y + k = 0
∴ We have:

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q23. Find the point on y-axis which is equidistant from the points (5, − 2) and (− 3, 2).

Sol. ∵ Let P is on the y-axis
∴ Coordinates of P are: (0, y)

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q24. The line joining the points (2, 1) and (5, − 8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0, find the value of k.

Sol.

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q25. If P (x, y) is any point on the line joining the points A (a, 0) and B (0, b), then show that:

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Sol. ä P lies on the line joining A and B.
∴ A, B and P are collinear.
⇒ The area of a Δ formed by A (a, 0), B (0, b) and P (x, y) is zero.
∴ We have:

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q. 26. Find the point on x-axis which is equidistant from the points (2, − 5) and (− 2, 9).

Sol. ∵ The required point ‘P’ is on x-axis.
∴ Coordinates of P are (x, 0).
∴ We have

AP = PB
⇒ AP2 = PB2
⇒ (2 − x)2 + (− 5 + 0)2 =(− 2 − x)2 + (9 − 0)2
⇒ 4 − 4x + x2 + 25 = 4 + 4x + x2 + 81
⇒ 4x + 25 = 4x + 81
⇒ − 8x = 56

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

∴ The required point is (−7, 0).

Q27. The line segment joining the points P (3, 3) and Q (6, − 6) is trisected at the points A and B such that A is nearer to P. It also lies on the line given by 2x + y + k = 0. Find the value of k.

Sol. ∵ PQ is trisected by A such that

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q28. Find the ratio in which the points (2, 4) divides the line segment joining the points A (− 2, 2) and B (3, 7). Also find the value of y.

Sol. Let P (2, y) divides the join of A (− 2, 2) and B (3, 7) in the ratio k:1
∴ Coordinates of P are:

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q29. Find the area of the quadrilateral ABCD whose vertices are: A (− 4, − 2), B (− 3, − 5), C (3, − 2) and D (2, 3)

Sol. Area of (Δ ABC)

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

  Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q30. Find the ratio in which the point (x, 2) divides the line segment joining the points (− 3, − 4) and (3, 5). Also find the value of x.

Sol. Let the required ratio = k : 1

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

∴ Coordinates of the point P are:

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

But the coordinates of P are (x, 2)

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q31. If P (9a – 2, –b) divides the line segment joining A (3a + 1, −3 ) and B (8a, 5) in the ratio 3 : 1, find the values of a and b.

Sol. ∵ P divides AB in the ratio 3 : 1
∴ Using the section formula, we have:

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

− b = 3 or b = −3
⇒ 36a − 8= 27a + 1 and b= −3
⇒ 9a = 9 and b = −3

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Thus, the required value of a = 1 and b = −3

Q32. Find the area of the triangle formed by joining the mid-points of the sides of triangle whose vertices are (0, − 1), (2, 1), and (0, 3).

Sol. We have the vertices of the given triangle as A (0, − 1), B (2, 1) and C (0, 3). Let D, E and F be the mid-points of AB, BC and AC.

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

∴ Coordinates of the vertices of Δ DEF are (1, 0), (1, 2) and (0, 1).

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q33. Find the area of the Δ ABC with A(1, –4), and the mid-point of sides through A being (2, –1) and (0, –1).

Sol. Let the coordinates of B and C are (a, b) and (x, y) respectively.
Sides through A are AB and AC

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Thus, the co-ordinates of the vertices of ΔABC are: A(1, –4), B(3, 2) and C(–1, 2)
∴ Area of ΔABC

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q34. Find the ratio in which the point (x, − 1) divides the line segment joining the points (− 3, 5) and (2, − 5). Also find the value of x. 

Sol. Let the required ratio is k : 1

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q35. Find the co-ordinates of the points which divide the line segment joining A(2, −3) and B(−4, −6) into three equal parts.

Sol. Let the required points are P(x1, y1) and Q(x2, y2)
 ∴ Using section formula, we have:

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Thus, the coordinates of the required points are (0, −4) and (−2, 5)

Q36. If the mid-point of the line segment joining the point A(3, 4) and B(k, 6) is P(x, y) and x + y – 10 = 0, then find the value of k.

Sol. ∵ Mid point of the line segment joining A(3, 4) and B(k, 6)

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

Q37. Point P, Q, R and S divide the line segment joining the points A (1, 2) and B (6, 7) in 5 equal parts. Find the co-ordinates of the points P, Q and R.

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

∴  P, Q, R and S, divide AB into five      equal parts.
∴ AP = PQ = QR = RS = SB
Now, P divides AB in the ratio 1 : 4    
Let, the co-ordinates of P be x and y.
∴ Using the section formula i.e.,
Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev
Next, Q divides AB in the ratio 2 : 3
∴ Co-ordinates of Q are :
Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev
Now, R divides AB in the ratio 3 : 2
⇒  Co-ordinates of R are :

Short Answer Type Questions(Part- 2)- Coordinate Geometry Class 10 Notes | EduRev

The co-ordinates of P, Q  and R are respectively:(2, 3), (3, 4) and (4, 5).

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