Question

if the distance between two points (k,2) and (3,4) is 8 then k=

Answer 1

solution.

we have distance formula=
$\sqrt{(x1 - x2)2 + (y1 - y2)2}$
=>
$\sqrt{(k - 3)2 + (2 - 4)2} = 8$
=> k^2+9-6k+ 4= 8

=> k^2 -6k+13 =8

=> k^2 -6k +5=0

=> k^2-5k -k+5=0

=> k(k-5) -1(k-5)=0

=> (k-1) (k-5)=0

=> k-1=0 or, k-5=0

=> k=1 or k = 5.

__________________

hope it help you☺☺☺

Answer 2

Answer:

10.745 or −4.745

Step-by-step explanation:

Given : Points (k,2) and (3,4)

To Find : if the distance between two points (k,2) and (3,4) is 8 then k=

Solution:

We will use distance formula :

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(x_1,y_1)=(k,2)$

$(x_2,y_2)=(3,4)$

$8=\sqrt{(3-k)^2+(4-2)^2}$

$8=\sqrt{9+k^2-6k+4}$

$64=k^2-6k+13$

$k^2-6k-51=0$

Now we will use discriminant formula to find k

Formula : $k=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$k^2-6k-51=0$

a = 1

b =-6

c =-51

Substitute the values in the formula :

$k=\frac{6\pm\sqrt{(-6)^2-4(1)(-51)}}{2(1)}$

$k=\frac{6\pm\sqrt{240}}{2}$

$k=\frac{6+\sqrt{240}}{2},\frac{6-\sqrt{240}}{2}$

$k=10.745,−4.745$

So, k can be 10.745 or −4.745