West Bengal Board Class 9 Math Solution Chapter 19 - Co-ordinate Geometry: Internal and External Division of Straight Line Segment

Find the co-ordinates of the point which divides the line segment joining two point s in the given ratio for the following:

(6, –4) and (–8, 10); in the ratio 3: 4 internally

Find the co-ordinates of the point which divides the line segment joining two point s in the given ratio for the following:

(5, 3) and (–7, –2); in the ratio 2: 3 internally

Find the co-ordinates of the point which divides the line segment joining two point s in the given ratio for the following:

(–1, 2) and (4, –5); in the ratio 3: 2 externally

Find the co-ordinates of the point which divides the line segment joining two point s in the given ratio for the following:

(3, 2) and (6, 5); in the ratio 2: 1 externally

Find the co-ordinates of mid-point of line segment joining two point s for the following

(i) (5, 4) and (3, –4)

(ii) (6, 0) and (0, 7)

Let us calculate the ratio in which the point (1, 3) divides the line segment joining the point s (4, 6) and (3, 5).

Let us calculate in what ratio is the line segment joining the point s (7, 3) and (–9, 6) divided by the y – axis.

Prove that when the point s A (7, 3), B (9, 6), C (10, 12) and D (8, 9) are joined in order, then they will form a parallelogram.

If the point s (3, 2), (6, 3), (x, y) and (6, 5) when joined in order and form a parallelogram, then let us calculate the point (x, y)

If (x₁, y₁), (x₂, y₂), (x₃, y₃) and (x₄, y₄) point s are joined in order to form a parallelogram, then prove that x₁ + x₃ = x₂ + x₄ and y₁ + y₃ = y₂ + y₄.