Question

Maths lovers! This is Rahul.

If A(3,6) and C (1,2) are the two vertices of rhombus ABCD. Then find the equation of the straight line that lies along BD which is a diagonal.

Answer 1

Let the vertices are A(3,6) and C(1,2)

In rhombus,
Diagonals bisects each other at right angles.

➡️Midpoint of AC = Midpoint of BD
and AC is perpendicular to BD

Midpoint of AC =
$( \frac{x1 + x2}{2} \: and \: \frac{y1 + y2}{2}$
$( \frac{4}{2} \: and \: \frac{6}{2} )$
$midpoint \: of \: bd = (2and4)$
Let the slope of BD be m2,
Since AC is perpendicular to BD,
m1×m2 = -1
2× m2 = -1
m2 = -2

By using slope point form,

$y - y1 = m(x - x1)$
$y - 4 = 2(x + 1)$
$y - 4 = 2x + 2$
Since the required equation. is,
2x- y +6

Hope it helps.