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 ** and is an equilateral triangle.

OR

Name the type of triangle PQR formed by the points and

**Q22. The line joining the points (2, âˆ’ 1) and (5, âˆ’ 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, âˆ’ 1) and B (5, âˆ’ 6).

âˆµ P is the mid point of AB,

âˆ´ Coordinates of P are:

Since P lies on the line 2x + 4y + k = 0

âˆ´ We have:

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

**Sol.** âˆµ Let P is on the y-axis

âˆ´ Coordinates of P are: (0, y)

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

**Sol.**

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

Sol. Ã¤ P lies on the line joining A and B.

âˆ´ A, B and P are collinear.

â‡’ The area of a Î” formed by A (a, 0), B (0, b) and P (x, y) is zero.

âˆ´ We have:

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

**Sol.** âˆµ The required point â€˜Pâ€™ is on x-axis.

âˆ´ Coordinates of P are (x, 0).

âˆ´ We have

AP = PB

â‡’ AP^{2} = PB^{2}

â‡’ (2 âˆ’ x)2 + (âˆ’ 5 + 0)2 =(âˆ’ 2 âˆ’ x)^{2} + (9 âˆ’ 0)^{2}

â‡’ 4 âˆ’ 4x + x^{2} + 25 = 4 + 4x + x^{2} + 81

â‡’ 4x + 25 = 4x + 81

â‡’ âˆ’ 8x = 56

âˆ´ The required point is (âˆ’7, 0).

**Q27. The line segment joining the points P (3, 3) and Q (6, âˆ’ 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. âˆµ PQ is trisected by A such that**

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

**Sol. **Let P (2, y) divides the join of A (âˆ’ 2, 2) and B (3, 7) in the ratio k:1

âˆ´ Coordinates of P are:

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

**Sol. Area of (Î” ABC)**

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

**Sol. **Let the required ratio = k : 1

âˆ´ Coordinates of the point P are:

But the coordinates of P are (x, 2)

**Q31. If P (9a â€“ 2, â€“b) divides the line segment joining A (3a + 1, âˆ’3 ) and B (8a, 5) in the ratio 3 : 1, find the values of a and b.**

**Sol. **âˆµ P divides AB in the ratio 3 : 1

âˆ´ Using the section formula, we have:

âˆ’ b = 3 or b = âˆ’3

â‡’ 36a âˆ’ 8= 27a + 1 and b= âˆ’3

â‡’ 9a = 9 and b = âˆ’3

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

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

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

âˆ´ Coordinates of the vertices of Î” DEF are (1, 0), (1, 2) and (0, 1).

**Q33. Find the area of the Î” ABC with A(1, â€“4), and the mid-point of sides through A being (2, â€“1) and (0, â€“1).**

**Sol. **Let the coordinates of B and C are (a, b) and (x, y) respectively.

Sides through A are AB and AC

Thus, the co-ordinates of the vertices of Î”ABC are: A(1, â€“4), B(3, 2) and C(â€“1, 2)

âˆ´ Area of Î”ABC

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

**Sol.** Let the required ratio is k : 1

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

**Sol. Let the required points are P(x _{1}, y_{1}) and Q(x_{2}, y_{2})**

âˆ´ Using section formula, we have:

Thus, the coordinates of the required points are (0, âˆ’4) and (âˆ’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 â€“ 10 = 0, then find the value of k.**

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

**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.**

âˆ´ P, Q, R and S, divide AB into five equal parts.

âˆ´ AP = PQ = QR = RS = SB

Now, P divides AB in the ratio 1 : 4

Let, the co-ordinates of P be x and y.

âˆ´ Using the section formula i.e.,

Next, Q divides AB in the ratio 2 : 3

âˆ´ Co-ordinates of Q are :

Now, R divides AB in the ratio 3 : 2

â‡’ Co-ordinates of R are :

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

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