Question

The distance between the points ( 2, -3 ) and ( k , 9 ) is 13 units. Find „k‟​

Answer 1

Step-by-step explanation:

hope this answer will be helpful

Answer 2

The value of k in the given point is k=7 or k=-3

Step-by-step explanation:

Given that the distance between the points (2,-3) and (k,9) is 13 units

To find the value of k :

Distance formula is $s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ units

Let $(x_1,y_1)$ and $(x_2,y_2)$ be the given points (2,-3) and (k,9) respectively and s=13 units

Substitute the values in the distance formula we get

$13=\sqrt{(k-2)^2+(9-(-3))^2}$

$13=\sqrt{(k-2)^2+(9+3)^2}$

$13=\sqrt{(k-2)^2+(12)^2}$

Squaring on both sides

$13^2=(\sqrt{(k-2)^2+(12)^2})^2$

$169=(k-2)^2+144$

$169-144=(k-2)^2$

$25=(k-2)^2$

$k^2-2(k)(2)+2^2=25$

$k^-4k+4-25=0$

$k^2-4k-21=0$

$(k-7)(k+3)=0$

Therefore k-7=0 or k+3=0

Therefore the value is k=7 or k=-3