Question

Example 6 If the line segment joining the points A(4, -5) and B(4, 5) is divided by the
point P such that AP/AB = 2/3
find the coordinates of P.
(חת​

Answer 1

$\bold \green{question}$

6. If the line segment joining the points A(4, -5) and B(4,5) is divided by the point P such that AP/AB = 2/3. Find the co-ordinate of P.

$\bold \green{answer}$

$\bold \orange{given} \: \: \bold \red{ \frac{ap}{ab} = \frac{2}{3}}$

$\bold \purple{↦} \: \bold \pink{ \frac{ab}{ap} = \frac{3}{2}} \\ \\ \bold \purple{⟼} \: \bold \pink{ \frac{ab}{ap} - 1 = \frac{3}{2} - 1} \\ \\ \bold \purple{ ⟼} \: \bold \pink{ \frac{pb}{ap} = \frac{1}{2}} \\ \\ \bold \purple{ } \: \bold \pink{coordinates \: of \: p}$

$= ( \frac{mx2 + nx1}{m + x} \: \: \frac{my2 + xy1}{m + x} ) \\ \\ = ( \frac{2 \times 4 + 3 \times 4}{2 + 3} \: \: \frac{2 \times 5 + 3 \times ( - 5)}{2 + 3}) \\ \\ = \frac{8 + 12}{5} \: \frac{10 -15 }{5} \\ \\ = (4 \: \: \: \: - 1)$

Coordinates of P = (4, -1)