Point P divides the line segment joining the points A (8, 0) and B (16, -8) in the ration 3:5. Find its co-ordinates of point P.

Also, find the equation of the line through P and parallel to 3x + 5y = 7.

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Solution

Using section formula, the co-ordinates of the point P are

$open parentheses fraction numerator 3 cross times 16 plus 5 cross times 8 over denominator 3 plus 5 end fraction comma fraction numerator 3 cross times negative 8 plus 5 cross times 0 over denominator 3 plus 5 end fraction close parentheses equals open parentheses 11 comma negative 3 close parentheses equals open parentheses x subscript 1 comma y subscript 1 close parentheses$

3x + 5y = 7

$y equals fraction numerator negative 3 over denominator 5 end fraction x plus 7 over 5$

Slope of this line = $fraction numerator negative 3 over denominator 5 end fraction$

As the required line is parallel to the line 3x + 5y = 7,

Slope of the required line = Slope of the given line = $fraction numerator negative 3 over denominator 5 end fraction$

Thus, the equation of the required line is

y - y₁ = m(x - x₁)

y + 3 = $fraction numerator negative 3 over denominator 5 end fraction$ (x - 11)

5y + 15 = -3x + 33

3x + 5y = 18

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