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RD Chapter 14- Co-ordinate Geometry Ex-14.5 Interview Questions Answers

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

Answer 1 : (i) Co-ordinates of ∆ABC are A (6, 3), B (-3, 5) and C (4, -2)

Question 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) (C.B.S.E. 2009)

Answer 2 :

(i) Let vertices of quadrilateral ABCD be A (-3, 2), B (5, 4), C (7, -6) and D (-5, -4)
Join AC

Question 3 : The four vertices of a quadrilaterals 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 ?

Answer 3 :

Let the vertices of quadrilateral ABCD be
A (1, 2), B (-5, 6), C (7, -4) and D (k, -2)
Join AC

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

Answer 4 :

Vertices of ∆ABC are A (-2, 1), B (5, 4) and C (2, -3) and AD ⊥ BC, let AD = h
Now area of ∆ABC