The coordinates of the points A, B, C are ( x_1 , y_1 ), ( x_2 , … - Vidyadip

MCQ

The coordinates of the points $A, B, C$ are $({x_1},{y_1})$, $({x_2},{y_2})$, $({x_3},\,{y_3})$ and $D$ divides the line $AB$ in the ratio $l : k$. If $P$ divides the line $DC$ in the ratio $m : k + l$, then the coordinates of $P$ are

✓
$\left( {\frac{{k{x_1} + l{x_2} + m{x_3}}}{{k + l + m}},\,\frac{{k{y_1} + l{y_2} + m{y_3}}}{{k + l + m}}} \right)$
B
$\left( {\frac{{l{x_1} + m{x_2} + k{x_3}}}{{l + m + k}},\,\frac{{l{y_1} + m{y_2} + k{y_3}}}{{l + m + k}}} \right)$
C
$\left( {\frac{{m{x_1} + k{x_2} + l{x_3}}}{{m + k + l}},\,\frac{{m{y_1} + k{y_2} + l{y_3}}}{{m + k + l}}} \right)$
D
None of these

✓

Answer

Correct option: A.

$\left( {\frac{{k{x_1} + l{x_2} + m{x_3}}}{{k + l + m}},\,\frac{{k{y_1} + l{y_2} + m{y_3}}}{{k + l + m}}} \right)$

a
(a) Coordinates of $D$ will be $\left( {\frac{{l{x_2} + k{x_1}}}{{l + k}},\,\,\frac{{l{y_2} + k{y_1}}}{{l + k}}} \right)$

Now again, $DC$ is divided by $P$ in $m:k + l.$

Then the coordinates of $P$ will be given by

$\left( {\frac{{m{x_3} + l{x_2} + k{x_1}}}{{k + l + m}},\,\frac{{m{y_3} + l{y_2} + k{y_1}}}{{k + l + m}}} \right)$.

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