First slide

Equation of line in Straight lines

Question

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

Moderate

A

$y = 2 x$
B

$y = x + 1$
C

$x + 2 y = 5$
D

$y = 3 x - 1$

Solution

Obviously, the line through $Q$ is at the greatest distance from point P when it is perpendicular to $PQ$ . Now, the slope of line $PQ$ . 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 $2 x - y = 0$

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