A point (4,4) divides the line segment joinin | vedclass

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Question

Solution:
Let the ratio in which the point $P(4,4)$ divides the line segment joining $A(2,6)$ and $B(6,2)$ be $k:1$.
Using the section formula, the

Vedclass · Accepted Answer

$1:1$

Vedclass · Answer

Solution:
Let the ratio in which the point $P(4,4)$ divides the line segment joining $A(2,6)$ and $B(6,2)$ be $k:1$.
Using the section formula, the coordinates of point $P$ are:
$P = \left( \frac{k(6) + 1(2)}{k+1}, \frac{k(2) + 1(6)}{k+1} \right) = (4,4)$
Equating the $x$-coordinates:
$\frac{6k + 2}{k+1} = 4$
$6k + 2 = 4k + 4$
$2k = 2$
$k = 1$
Thus, the ratio $k:1$ is $1:1$.
Alternatively:
The midpoint of $AB$ is:
$\left( \frac{2+6}{2}, \frac{6+2}{2} \right) = (4,4)$
Hence, the point $(4,4)$ is the midpoint, dividing the segment in the ratio $1:1$.

$A$ point $(4,4)$ divides the line segment joining $A(2,6)$ and $B(6,2)$ from $A$,then the ratio of division is $\ldots \ldots \ldots \ldots .$

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