Question

If A and B are (1, 4) and (5, 2) respectively, find the coordinates of P when AP/BP = 3/4.

Answer 1

Answer:

The point P divides AB in the ratio 3 : 4

m : n = 3 : 4

P = (mx2 + nx1) / (m+n) , (my2 + ny1) / (m+n)

A = (x1,y1) = (1,4) ; B = (x2,y2) = (5,2)

P = [ 15+4 / 7 , 6+16/7] = [19/7 , 22/7]

Step-by-step explanation:

please Mark as

Answer 2

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 3 : 4

A ∘──────────|───────────∘ B

(1,4) ⠀⠀⠀⠀⠀⠀⠀⠀ P ⠀⠀⠀⠀⠀⠀⠀⠀⠀(5,2)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Here,

$\sf A = x_1 = 1 , y_1 = 4$

$\sf B = x_2 = 5 , y_2 = 2$

$\sf m = 3 , n = 4$

$\sf \dfrac{AP}{BP} = \dfrac{3}{4}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀

• Using section formula,

⠀⠀⠀⠀⠀⠀⠀

$\star\;{\boxed{\sf{\purple{ x\;,\;y = \bigg( \dfrac{m_2 x_1 + m_1 x_2 }{m_1 + m_2 }\;,\; \dfrac{m_2 y_1 + m_1 y_2 }{m_1 + m_2 } \bigg)}}}}$

$:\implies\sf \bigg( \dfrac{3 \times 5 + 4 \times 1}{3+4}\;,\; \dfrac{3 \times 2 + 4 \times 4}{3 + 4} \bigg)$

$:\implies\sf \bigg( \dfrac{15+4}{7}\;,\; \dfrac{6 + 16}{7} \bigg)$

$:\implies\sf \bigg( \dfrac{19}{7}\;,\; \dfrac{22}{7}\bigg)$

$:\implies{\boxed{\frak{\pink{ \bigg( \dfrac{19}{7}\;,\; \dfrac{22}{7}\bigg)}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;the\;coordinates\;of\;P\;will\;be\; \bf{\bigg( \dfrac{19}{7}\;,\; \dfrac{22}{7}\bigg) }.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━