Question

which of the follIf the point P divides the line segment AB (A(x_1, y_1) and B(x_2, y_2)) externally in the ratio of m : n then y coordinate of the point P is ________owing are not objectives of providing depreciation

Answer 1

SOLUTION

GIVEN

The point P divides the line segment AB (A(x₁ , y₁ ) and B(x₂, y₂)) externally in the ratio of m : n

TO DETERMINE

The y coordinate of the point P

CONCEPT TO BE IMPLEMENTED

$\sf{The \: coordinate \: of \: the \: point \: where \: the \: line }$ $\sf{joining \: the \: points \: (x_1,y_1) \: and \: (x_2,y_2) \: }$ externally divided in $\sf{the \: ratio \: \: m :n \: \: is }$

$\displaystyle \sf{ \bigg( \frac{mx_2 - nx_1 \: }{m - n} \: \: , \: \frac{my_2 - ny_1 \: }{m + n} \bigg) }$

EVALUATION

Here the given points are A(x₁ , y₁ ) and B(x₂, y₂)

Now the line line segment AB (A(x₁ , y₁ ) and B(x₂, y₂)) externally in the ratio of m : n

So the coordinates of the point P is

$\displaystyle \sf{ = \bigg( \frac{mx_2 - nx_1 \: }{m - n} \: \: , \: \frac{my_2 - ny_1 \: }{m - n} \bigg) }$

Hence the required y coordinate of the point P

$\displaystyle \sf{ = \frac{my_2 - ny_1 \: }{m - n} }$

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