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RD Chapter 14- Co-ordinate Geometry Ex-14.4 Interview Questions Answers

Question 1 :
Find the centroid of the triangle whose vertices are :
(i) (1, 4), (-1, -1), (3, -2)
(ii) (-2, 3), (2, -1), (4, 0)

Answer 1 :


Question 2 : Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the Co-ordinates of the third vertex.

Answer 2 :

Centroid of a triangle is O(0, 0) ….(i)
Co-ordinates of two vertices of a ∆ABC are A (1, 2) and B (3, 5)
Let the third vertex be (x, y)

Question 3 : Find the third vertex of a triangle, if two of its vertices are at (-3, 1) and (0, -2) and the centroid is at the origin.

Answer 3 :

Let two vertices of a ∆ABC be A (-3, 1) and B (0, -2) and third vertex C be (x, y)
Centroid of the ∆ABC is O (0, 0)

Question 4 : A (3, 2) and B (-2, 1) are two vertices of a triangle ABC whose centroid G has the coordinates (5/3 , −1/3) . Find the coordinates of the third vertex C of the triangle. [CBSE 2004]

Answer 4 :

A (3, 2) and B (-2, 1) are the two vertices of ∆ABC whose centroid is G (5/3 , −1/3)
Let third vertex C be (x, y)

Question 5 : If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the co-ordinates of its centroid.

Answer 5 : In ∆ABC, D, E and F are the mid-points of the sidesBC, CA and AB respectively.
The co-ordinates of D are (-2, 3), of E are (4,-3) and of F are (4, 5)
Let the co-ordinates of A, B and C be (x1, y1),(x2, y2), (x3, y3)respectively

Question 6 : Prove analytically that the line segment joining the middle points of two sides of a triangle is equal to half of the third side.

Answer 6 :

In ∆ABC,
D and E are the mid points of the sides AB and AC respectively

Question 7 : Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the join of the middle points of its diagonals meet in a point and bisect one another.

Answer 7 :

Let A (x1, y1), B (x2, y2), C (x3, y3) and D (x4, y4) be the vertices of quadrilateral ABCD
E and F are the mid points of side BC and AD respectively and EF is joined G and H are the mid points of diagonal AC and BD.
GH are joined