Question

if the distance between two points (x,7) and (1,15) is 10.find x

Answer 1

Using the distance formula
10=√(x-1)^2+(15-7)^2
10=√(x-1)^2+64
100=(x-1)^2+64
(x-1)^2=36
→(x-1)=±6

so x=7 or -5

Answer 2

Answer:

-5 or 7

Step-by-step explanation:

Two Points :

$(x_1,y_1)=(x,7)$

$(x_2,y_2)=(1,15)$

We are given that  the distance between two points (x,7) and (1,15) is 10

So, to find x we will use distance formula:

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

$(x_1,y_1)=(8,-5)$

$(x_2,y_2)=(-2,-7)$

Substitute the values in the formula :

$10=\sqrt{(1-x)^2+(15-7)^2}$

$10=\sqrt{1+x^2-2x+(8)^2}$

$10^2=1+x^2-2x+64$

$100=x^2-2x+65$

$x^2-2x-35 =0$

$x^2-7x+5x-35 =0$

$x(x-7)+5(x-7) =0$

$(x+5)(x-7) =0$

$x=-5,7$

Hence the value of x is -5 or 7