# Find the Coordinates of Point P If P Divides the Line Segment Joining the Points A(–1,7) and B(4,–3) in the Ratio 2 : 3. - Geometry

Sum

Find the coordinates of point P if P divides the line segment joining the points A(–1,7) and B(4,–3) in the ratio 2 : 3.

#### Solution

Let the coordinates of point P be (x, y).
The ratio in which P divides A(–1,7) and B(4,–3) is 2 : 3.
Using the section formula we have

$x = \frac{4 \times 2 + 3 \times \left( - 1 \right)}{2 + 3} = \frac{8 - 3}{5} = 1$

$y = \frac{2 \times \left( - 3 \right) + 3 \times 7}{2 + 3} = \frac{- 6 + 21}{5} = 3$

Thus, the coordinates of point P are (1, 3).

Concept: The Mid-point of a Line Segment (Mid-point Formula)
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#### APPEARS IN

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 5 Co-ordinate Geometry
Practice Set 5.2 | Q 1 | Page 115