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9.Straight Line
easy
The point moves such that the area of the triangle formed by it with the points $(1, 5)$ and $(3, -7)$ is $21$ sq. unit. The locus of the point is
A
$6x + y - 32 = 0$
B
$6x - y + 32 = 0$
C
$x + 6y - 32 = 0$
D
$6x - y - 32 = 0$
Solution
(a) Let the point be $(x,\,y).$ Area of triangle with points $(x,\,y),\,(1,\,5)$ and $(3,\, – 7)$ is $21$ sq. units
$\frac{1}{2}\left| {\,\begin{array}{*{20}{c}}x&y&1\\1&5&1\\3&{ – 7}&1\end{array}} \right| = 21$
Solving; locus of point $(x,\,y)$ is $6x + y – 32 = 0$.
Standard 11
Mathematics
