Question

The distance between the points (4, 8) and (k, -2) is 10 units. Find the value of k.

Answer 1

Distance between points $(x_1,y_1)$ and $(x_2,y_2)=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\sqrt{(k-4{)}^2+(-2-8{)}^2}=10$

$\Rightarrow$ $\sqrt{(k-4{)}^2+100}=10$

Squaring both the sides

$\Rightarrow$ $(k-4{)}^2+100=100$

$\Rightarrow$ $(k-4{)}^2=0$

$\Rightarrow k-4=0$

$\Rightarrow k=4$