Coordinate Geometry Exercise 14.4 – Questions:
- In what ratio does the point (-2, 3) divide the line segment joining the points (-3, 5) and (4, -9)?
- In the point C(1, 1) divides the line segment joining A(-2, 7) and B in the ratio 3:2, find the coordinates of B.
- Find the ratio in which the point (-1, k) divides the line joining the points (-3, 10) and (6, -8) and find the value of k.
- Find the coordinates of the midpoint of the line joining the points (-3, 10) and (6, -8).
- Three consecutive vertices of a parallelogram are A(1, 2), B(2, 3) and C(8, 5). Find the fourth vertex. [Hint: diagonals of a parallelogram bisect each other]
Coordinate Geometry Exercise 14.4 – Solutions:
- In what ratio does the point (-2, 3) divide the line segment joining the points (-3, 5) and (4, -9)?
Solution:
Let the required ratio be m:n
Given: (x1, y1) = (-2, 3), (x2, y2) = (4, -9) and (x , y) = (-2, 3)
By section formula,
- In the point C(1, 1) divides the line segment joining A(-2, 7) and B in the ratio 3:2, find the coordinates of B.
Solution:
Let the required ratio be m:n
Given: (x1, y1) = (-2, 7) , m:n = 3:2 and (x , y) = (1, 1) . We have to find (x2, y2).
By section formula,
To find x2,
To find y2,
Therefore, (x2, y2) = (3, -3) .Hence B(3, -3).
- Find the ratio in which the point (-1, k) divides the line joining the points (-3, 10) and (6, -8) and find the value of k.
Solution:
Given, (x, y)= (-1, k), (x1, y1) = (-3, 10) and (x2, y2) = (6, -8)
By section formula,
To find m:n,
To find y2,
Therefore, m:n = 2:7 and k = 6.
- Find the coordinates of the midpoint of the line joining the points (-3, 10) and (6, -8).
Solution:
Given, (x1, y1) = (-3, 10) and (x2, y2) = (6, -8).
- Three consecutive vertices of a parallelogram are A(1, 2), B(2, 3) and C(8, 5). Find the fourth vertex. [Hint: diagonals of a parallelogram bisect each other]
Solution:
Given, A(1, 2), B(2, 3) and C(8, 5)
Diagonal of a parallelogram bisect each other. Therefore, diagonal of the parallelogram is the midpoint.
We know, diagonals of the parallelogram are equal.
Therefore, we have, (9/2, 7/2) = (2+x/2, 3+y/2)
Then,
Also