Question

The value of k when the distance between the origin and (2,k) is √173 cm is

Answer 1

Answer:

value of k are 13, -13

Step-by-step explanation:

whole under root(2-0)^2 + (k-0)^2

distance given=√173

so equation formed,

whole under root ( (2-0)^2+(k-0)^2 )= √173

by multiplying square on both sides

(2)^2+(k)^2=173

4+k^2= 173

k^2 = 169

k = √169

k= + - 13

k = 13 , -13

Answer 2

$\LARGE{ \underline{ \pink{ \sf{Required \: answer:}}}}$

The distance between any two coordinates in a Cartesian plane can be solved by using the distance formula.

$\large{ \because{ \underline{ \boxed{ \rm{d = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} } }}}}}$

GiveN:

• Origin (0,0)
• Point P(2,k)
• Distance between O and P = √173 cm

By using Distance formula,

⇛ $\rm{\sqrt{(2 - 0) {}^{2} + (k - 0) {}^{2}} = \sqrt{173} }$

This is equals to,

⇛ $\rm{ \sqrt{ {2}^{2} + {k}^{2} } = \sqrt{173} }$

Squaring both sides,

⇛ $\rm{ {2}^{2} + {k}^{2} = 173}$

Isolating k² on the LHS by subtracting 2² from RHS,

⇛ $\rm{ {k}^{2} = 169}$

⇛ $\rm{k = \pm 13}$

$\therefore$Thus, the value of k in the coordinate can be +13 or -13.