Co­ordinate Geometry Exercise 14.1 (Part-12) | Extra Documents, Videos & Tests for Class 10 PDF Download

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 : 

We know area of triangle formed by three points is given by 

(i) The vertices are given as (6, 3), (−3, 5), (4, −2).

(ii) The vertices are given as .

(iii) The vertices are given as .

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)

Answer :

(i) Let the vertices of the quadrilateral be A (−3, 2), B (5, 4), C (7, −6), and D (−5, −4). Join AC to form two triangles ΔABC and ΔACD.

(ii) Let the vertices of the quadrilateral be A (1, 2), B (6, 2), C (5, 3), and D (3, 4). Join AC to form two triangles ΔABC and ΔACD.

(iii) Let the vertices of the quadrilateral be A (−4, −2), B (−3, −5), C (3, −2), and D (2, 3). Join AC to form two triangles ΔABC and ΔACD.

Question 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.

Answer  :

GIVEN: The four vertices of quadrilateral are (1, 2), (−5, 6), (7, −4) and D (k, −2) taken in order. If the area of the quadrilateral is zero

TO FIND: value of k

PROOF: Let four vertices of quadrilateral are A (1, 2) and B (−5, 6) and C (7, −4) and D (k, −2)

We know area of triangle formed by three points is given by

Now Area of ΔABC

Taking three points when A (1, 2) and B (−5, 6) and C (7, −4)

Also,

Now Area of ΔACD

Taking three points when A (1, 2) and C (7, −4) and D (k, −2)

Hence