In what ratio does the $y$ -axis divide the line segment joining A(−5, 3) and B(3, −7)?

Class 10Coordinate GeometryGeometry — Coordinates

Step-by-Step Solution

On the

y

-axis the X-coordinate is 0 (setting

y = 0

instead is the classic slip — that is the

x

-axis condition). Let the ratio be

k : 1 : \frac{k \cdot 3 + 1 \cdot ( - 5 )}{k + 1} = 0

→

3 k - 5 = 0

→

k = \frac{5}{3}

, so the ratio is 5 : 3. Writing

k

upside down gives 3 : 5; 5 : 8 compares the first part with the whole segment instead of with the second part.

Answer: B) 5:3

**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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