MENU

RD Chapter 14 Co ordinate Geometry Ex 14.3 Solutions

Question - 51 : - If the co-ordinates of the mid-points of the sides of a triangle be (3, -2), (-3, 1) and (4, -3), then find the co-ordinates of its vertices.

Answer - 51 : -

In a ∆ABC,
D, E and F are the mid-points of the sides BC, CA and AB respectively and co-ordinates of D, E and F are (3, -2), (-3, 1) and (4, -3) respectively

Question - 52 : - The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q. If the co-ordinates of P and Q are (p, -2) and (5/3 , q) respectively, find the values of p and q. [CBSE 2005]

Answer - 52 : -


Question - 53 : - The line joining the points'(2, 1), (5, -8) is trisected at the points P and Q. If point P lies on the line 2x – y + k = 0, find the value of k. [CBSE 2005]

Answer - 53 : - Points A (2, 1), and B (5, -8) are the ends points of the line segment AB

Question - 54 : -
A (4, 2), B (6, 5) and C (1, 4) are the vertices of ∆ABC,
(i) The median from A meets BC in D. Find the coordinates of the point D.
(ii) Find the coordinates of point P on AD such that AP : PD = 2 : 1.
(iii) Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What do you observe? [NCERT,CBSE, 2009, 10]

Answer - 54 : -

In ∆ABC, co-ordinates of A (4, 2) of (6, 5) and of (1, 4) and AD is BE and CF are the medians such that D, E and F are the mid points of the sides BC, CA and AB respectively
P is a point on AD such that AP : PD = 2 : 1
(iv) We see that co-ordinates of P, Q and R are same i.e., P, Q and R coincides eachother. Medians of the sides of a triangle pass through the same point which is called the centroid of the triangle.

Question - 55 : - If the points A (6, 1), B (8, 2), C (9, 4) and D (k, p) are the vertices of a parallelogram taken in order, then find the values of k and p.

Answer - 55 : -

The diagonals of a parallelogram bisect each other
O is the mid-point of AC and also of BD
O is the mid-point of AC

Question - 56 : - A point P divides the line segment joining the points A (3, -5) and B (-4, 8) such that AP/PB = k/1. If P lies on the line x + y = 0, then find the value of k. [CBSE 2012]

Answer - 56 : - Point P divides the line segment by joining the points A (3, -5) and B (-4, 8)

Question - 57 : - The mid-point P of the line segment joining the points A (-10, 4) and B (-2, 0) lies on the line segment joining the pionts C (-9, -4) and D (-4, y). Find the ratio in which P divides CD. Also, find the value of y. [CBSE 2014]

Answer - 57 : -

P is the mid-point of line segment joining the points A (-10, 4) and B (-2, 0)
Coordinates of P will be

=> y = 18/3 = 6
y = 6

Question - 58 : - If the point C (-1, 2) divides internally the line segment joining the points A (2, 5) and B (x, y) in the ratio 3 : 4, find the value of x² + y². [CBSE 2016]

Answer - 58 : -


Question - 59 : - ABCD is a parallelogram with vertices A (x1, y1), B (x2, y2) and C (x3, y3). Find the coordinates of the fourth vertex D in terms of x1, x2, x3, y1, y2 and y3. [NCERT Exemplar]

Answer - 59 : - Let the coordinates of D be (x, y). We know that diagonals of a parallelogram bisect each other.

Question - 60 : -
The points A (x1, y1), B (x2, y2) and C (x3, y3) are the vertices of ∆ABC.
(i) The median from A meets BC at D. Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.
(iii) Find the points of coordinates Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What are the coordinates of the centroid of the triangle ABC? [NCERT Exemplar]

Answer - 60 : -

Given that, the points A (x1, y1), B (x2, y2) and C (x3, y3) are the vertices of ∆ABC.
(i) We know that, the median bisect the line segment into two equal parts i.e., here D is the mid-point of BC.

Free - Previous Years Question Papers
Any questions? Ask us!
NodeJS Interview Questions Answers
ASP.Net Interview Questions Answers
Interview Questions Answers
×