First slide

Equation of line in Straight lines

Question

A line perpendicular to the line segment joining the points $(7, 3)$ and $(3, 7)$ divides it in the ratio $1 : 3$ , the equation of the line is

Moderate

A

$x + y - 10 = 0$
B

$x - y + 4 = 0$
C

$x - y + 2 = 0$
D

$x - y - 2 = 0$

Solution

Slope of the given line is $\frac{7 - 3}{3 - 7} = - 1$ and the coordinates of the point which divides the given line segment in the ratio $1 : 3$ is $(\frac{1 \times 3 + 3 \times 7}{4}, \frac{1 \times 7 + 3 \times 3}{4}) = (6, 4)$
So equation of the line passing through the point (6, 4) and perpendicular to the given line is
$y - 4 = x - 6 \Rightarrow x - y - 2 = 0 .$

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