In what ratio does the point (−4, 6) divide the line segment joining A(−6, 10) and B(3, −8)?

Class 10Coordinate GeometryGeometry — Coordinates

Step-by-Step Solution

Let ratio be

k : 1. x = \frac{3 k - 6}{k + 1} = - 4

→

3 k - 6 = - 4 k - 4

→

7 k = 2

→

k = \frac{2}{7}

. So the ratio is 2:7.

Answer: A) 2:7

**Section formula (internal)**:
A point

P

dividing segment

A B

in ratio

m : n (P

closer to A means

m

smaller) has coordinates:

P = (\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})

Where

A = (x

₁,

y

₁),

B = (x

₂,

y

₂).

**Midpoint** is the special case

m = n : M = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})

.

**Example**: Find the point dividing

A B

in ratio 2:3 where

A = (1, 5), B = (6, - 5) . x = \frac{2 \cdot 6 + 3 \cdot 1}{5} = \frac{15}{5} = 3. y = \frac{2 \cdot ( - 5 ) + 3 \cdot 5}{5} = \frac{5}{5} = 1

.
Point: (3, 1).

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