RD Chapter 14 Co ordinate Geometry Ex 14.5 Solutions
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
Question - 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)
Answer - 5 : -
We know that points are collinear if the area of the triangle formed by them is zero
(a) Vertices of ∆ABC are (2, 5), (4, 6) and (8, 8)
Question - 6 : - Find the area of a quadrilateral ABCD, the coordinates of whose varities are A (-3, 2), B (5, 4), C (7, -6) and D (-5, -4). [CBSE 2016]
Answer - 6 : -
Area of quadrilateral ABCD
= area of ∆ABC + area of ∆ACD
Question - 7 : - In ∆ABC, the coordinates of vertex A are (0, -1) and D (1, 0) and E (0, 1) respectively the mid-points of the sides AB and AC. If F is the mid-point of side C, find the area of ∆DEF. [CBSE 2016]
Answer - 7 : -
Let B (p, q), C (r, s) and F (x, y)
Mid-point of AB = Coordinates of D
Question - 8 : - Find the area of the triangle PQR with Q (3, 2) and the mid-points of the sides through Q being (2, -1) and (1, 2). [CBSE 2015]
Answer - 8 : - In ∆PQR, L and N are mid points of QR and QP respectively coordinates of Q are (3, 2) of L are (2, -1) and of N are (1, 2)
Question - 9 : - If P (-5, -3), Q (-4, -6), R (2, -3) and S (1, 2) are the vertices of a quadrilateral PQRS, find its area. [CBSE 2015]
Answer - 9 : -
P (-5, -3), Q (-4, -6), R (2, -3) and S (1,2) are the vertices of a quadrilateral PQRS
Join PR which forms two triangles PQR and PSR
Question - 10 : - If A (-3, 5), B (-2, -7), C (1, -8) and D (6, 3) are the vertices of a quadrilateral ABCD, find its area. [CBSE 2014]
Answer - 10 : -
A (-3, 5), B (-2, -7), C (1,-8) and D (6, 3) are the vertices of a quadrilateral ABCD
Join AC