Question 11 Mark
If the distance between the points $(4, k)$ and $(1,0)$ is $5 ,$ then what can be the possible values of $k$ ?
Answer
View full question & answer→We know that distance $d$ between two points is given by
$d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$
It is given that the distance between the two points is $5$ Putting the values
$\Rightarrow 5=\sqrt{(4-1)^2+(k-0)^2}$
On squaring both sides,
$\Rightarrow 25=9+k^2$
$\Rightarrow 25-9=k^2$
$\Rightarrow 16=k^2$
$\Rightarrow k= \pm 4$
Hence, the possible values of $k$ are $4$ and $-4 .$
$d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$
It is given that the distance between the two points is $5$ Putting the values
$\Rightarrow 5=\sqrt{(4-1)^2+(k-0)^2}$
On squaring both sides,
$\Rightarrow 25=9+k^2$
$\Rightarrow 25-9=k^2$
$\Rightarrow 16=k^2$
$\Rightarrow k= \pm 4$
Hence, the possible values of $k$ are $4$ and $-4 .$
