Question

If the distance of paint A(3,k) is 5 from the origin, find the value of k​

Answer 1

$\sf\huge\bold{Answer:}$

Given :

point A(3,k)

origin O (0,0)

Distance between point A and origin O i.e AO = 5units

To find :

Value of k

Solution :

Distance formula

$:⟶d = \sqrt{( { x_{2} - x_{1})}^{2} + (y_{2} - y_{1}) {}^{2} }$

where

${x_{1}}$ = 3 ( x coordinate of point A )

${x_{2}}$ = 0 ( x coordinate of origin O )

${y_{1}}$ = k ( y coordinate of point A )

${y_{2}}$ = 0 ( y coordinate of origin O )

Distance AO = 5 units

Inserting values in distance formula

$:⟶AO = \sqrt{( { 0-3)}^{2} + (0 - k) {}^{2} }$

$:⟶5 = \sqrt{( { -3)}^{2} + ( - k) {}^{2} }$

$:⟶5 = \sqrt{ 9 + ( - k) {}^{2} }$

Squaring both sides

$:⟶(5) {}^{2} = (\sqrt{9 + ( - k) {}^{2} }) {}^{2}$

$:⟶25 = 9 + ( - k) {}^{2}$

$:⟶25 - 9 = ( - k) {}^{2}$

$:⟶16 = ( -1) {}^{2} (k) {}^{2}$

$:⟶16 = k{}^{2} \times 1$

$:⟶k = \sqrt{16}$

$:⟶k = \sqrt{4 \times 4}$

$:⟶k = 4$

Value of k = 4 units.