1.

Write down the equation of the line whose gradient is 3/2 and which passes through P where P divides the line segment joining A(-2, 6) and B(3, -4) in the ratio 2:3​

Answer» AVE line segments JOINING A(-2,6) and B(3,-4) in the ratio 2:3 as:

\circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 2 \times 3+3 \times (-2) }{2+3} , \dfrac{2 \times (-4) + 3 \times 6}{2+3} \right) }} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 6+(-6) }{5} , \dfrac{-8+18}{5} \right) }} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 6-6 }{5} , \dfrac{10}{5} \right) }} \\ \\ \\ \colon\implies{\sf{ P = \left( \dfrac{ 0 }{5} , 2 \right) }} \\ \\ \\ \colon\implies{\sf{ P = (0 , 2) }}

~Equation of line SEGMENT having gradient (m) = {\sf{ \dfrac{3}{2} }}

Line segment PASSES through P(0,2)

  • x = 0 \longrightarrow x - 0 = 0
  • y = 2 \longrightarrow y - 2 = 0

\dag \ {\pmb{\underline{\sf\green{ According \ to \ Equation: }}}} \\ \\ \colon\implies{\sf{ y-2 = \dfrac{3}{2} (x-0) }} \\ \\ \\ \colon\implies{\sf{ y-2 = \dfrac{3x-0}{2} }} \\ \\ \\ \colon\implies{\sf{ 2(y-2) = 3x }} \\ \\ \\ \colon\implies{\sf{ 2y-4 = 3x }} \\ \\ \\ \colon\implies{\sf{ 2y-3x = 4 }} \\

Hence,

{\underline{\sf{The \ equation \ of \ the \ line \ is \ 2y-3x = 4 . }}}


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