# Chapter 14 Co-Ordinate Geometry RD Sharma Solutions Exercise 14.5 Class 10 Maths

 Chapter Name RD Sharma Chapter 14 Co-Ordinate Geometry Book Name RD Sharma Mathematics for Class 10 Other Exercises Exercise 14.1Exercise 14.2Exercise 14.3Exercise 14.4 Related Study NCERT Solutions for Class 10 Maths

### Exercise 14.5 Solutions

1. Find the area of a triangle whose vertices are
(i) (6, 3), (-3, 5) and (4, -2)
(ii) [(at21 , 2at1 ), (at22 , 2at2 ) (at23 , 2at3)]
(iii) (a, c + a), (a, c) and (-a, c- a)

Solution

2. Find the area of the quadrilaterals, the coordinates of whose vertices are
(i) (-3, 2), (5, 4), (7, -6) and (-5, -4)
(ii) (1, 2), (6, 2), (5, 3) and (3, 4)
(iii) (-4, -2), (-3, -5), (3, -2), (2, 3)

Solution

(ii)
(iii)

3. The four vertices of a quadrilateral are (1, 2), (-5, 6), (7, -4) and (k, -2) taken in order. If the area of the quadrilateral is zero, find the value of k.
Solution

4. The vertices of Î”ABC are (-2, 1), (5, 4) and (2, -3) respectively. Find the area of the triangle and the length of the altitude through A.
Solution

5. Show that the following sets of points are collinear.
(a) (2, 5), (4, 6) and (8, 8)
(b) (1, -1), (2, 1) and (4, 5)
Solution
(a) Let A(2, 5), B(4, 6) and C(8, 8) be the given points
Area of Î”ABC

6. Prove that the points (a, 0), (0, b) and (1, 1) are collinear if, 1/a + 1/b = 1.
Solution
Let A(a, 0), B(0, b) and C(1, 1) be the given points
Area of Î”ABC

7. The point A divides the join of P (-5, 1) and Q (3, 5) in the ratio k : 1. Find the two values of k for which the area of Î”ABC where B is (1, 5) and C(7, -2) is equal to 2 units.
Solution

8. The area of a triangle is 5. Two of its vertices are (2, 1) and (3, -2). Third vertex lies on y =
x + 3. Find the third vertex.
Solution

9. If a ≠ b ≠ c, prove that the points (a, a2), (b, b2), (c, c2) can never be collinear.
Solution

10. Four points A(6, 3), B(-3, 5), C(4, -2) and D(x, 3x) are given in such a way that Î”DBC/Î”ABC = 1/2, find x.
Solution

11. For what value of a point (a, 1), (1, -1) and (11, 4) are collinear ?
Solution

12. Prove that the points (a, b), (a1 , b1 ) and (a – a1 , b – b1 ) are collinear if ab1 = a1b
Solution