Question

In the diagram, above,OKLM is a rhombus.

i)State the coordinates of M.

ii)Find the equation of line KO.

iii)Find the equation of line KL.​​​

Answer 1

url kota hoga na to usi din di ko bhee nahin

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

OKLM is a rhombus and Coordinates of K is ( -5, 12 ).

Since,

O is origin, So Coordinates of O is ( 0, 0 ).

We know,

Distance Formula :-

The distance between the points A (x₁ , y₁ ) and B (x₂ , y₂)

$\boxed{ \rm \: AB = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} }}$

So,

Length OK of rhombus is

$\rm :\longmapsto\:OK = \sqrt{ {(12 - 0)}^{2} + {( - 5 - 0)}^{2} }$

$\rm :\longmapsto\:OK = \sqrt{ 144 + 25 }$

$\rm :\longmapsto\:OK = \sqrt{ 169 }$

$\bf\implies \:OK = 13 \: units$

Now, we know that

↝All sides of rhombus are equal.

↝So, OK = OM = 13 units.

↝Now, M lies on x - axis in its negative direction and distance from the origin is 13 units.

↝ Coordinates of M = ( - 13, 0 ).

Now, To find equation of KO

We know,

Equation of line passing through the points A (x₁ , y₁ ) and B (x₂ , y₂) using two point form of a line is

$\boxed{ \rm \: y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)}$

Here,

↝Coordinates of O is ( 0, 0 )

and

↝Coordinates of K is ( - 5, 12 ).

Hence,

↝Equation of line OK using two point form is given by

$\rm :\longmapsto\:y - 0 = \dfrac{12 - 0}{ - 5 - 0}(x - 0)$

$\rm :\longmapsto\:y= \dfrac{12}{ - 5}x$

$\rm :\longmapsto\: - 5y = 12x$

$\rm :\longmapsto\: 12x + 5y = 0$

To find, Equation of KL

We know,

Equation of line parallel to x - axis and passing through the point ( a, b ) is given

$\boxed{ \rm \: y \: = \: b \: }$

Now, equation of KL passing through K ( - 5, 12 ) and parallel to x - axis Is

$\bf :\implies\:y \: = \: 12$