First slide

Equation of line in Straight lines

Question

Given $A \equiv (1, 1)$ and AB is any line through it cutting the x-axis at B. If AC is perpendicular to AB and meets the y-axis in C, then the equation of the locus of midpoint P of BC is

Moderate

A

$x + y = 1$
B

$x + y = 2$
C

$x + y = 2 xy$
D

$2 x + 2 y = 1$

Solution

The equation of line AB is $y - 1 = m (x - 1) .$ Therefore , the equation of line AC is
$y - 1 = \frac{1}{m} (x - 1)$
$2 h = 1 - \frac{1}{m}$
$2 k = 1 + \frac{1}{m}$
Eliminating m, we have locus $x + y = 1$

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