The equation of a line through the point (1,2) whose distance from the point (3,1) has the greatest value is

Question

The equation of a line through the point (1,2) whose distance from the point (3,1) has the greatest value is (A) y=2 x (B) y=x+1 (C) x+2 y=5 (D) y=3 x-1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/87095c635eeafee6a99061de2dbd2073-.png" /> Obviously, the line through Q is at the greatest distance from point P when it is perpendicular to P Q. Now, the slope of line P Q is mP Q =-1 / 2. Then the slope of perpendicular line passing through Q is y-2=2(x-1) or 2 x-y=0

Q. The equation of a line through the point $(1, 2)$ whose distance from the point $(3, 1)$ has the greatest value is

$y = 2 x$

$y = x + 1$

$x + 2 y = 5$

$y = 3 x - 1$

Obviously, the line through $Q$ is at the greatest distance from point $P$ when it is perpendicular to $PQ$ . Now, the slope of line $PQ$ is $m_{PQ}$ $= - 1/2$ . Then the slope of perpendicular line passing through $Q$ is
$y - 2 = 2 (x - 1)$
or $2 x - y = 0$

Q. The equation of a line through the point (1,2) whose distance from the point (3,1) has the greatest value is

y=2x

y=x+1

x+2y=5

y=3x−1