Answer:
the sum of all possible values of x is: 2+6 = 8
Step-by-step explanation:
Assume the two points in your question are:
=> The distance between the points A(x,21) and B(4,7) is [tex]10\sqrt{2}[/tex]
As we know, the distance of two points can be determined by this formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Apply this formula in this situation to find all possible values of x, we have:
[tex]\sqrt{(4-x)^{2} + (7-21)^{2} }[/tex] = [tex]\frac{10}{\sqrt{2} }[/tex]
<=> [tex](4-x)^{2} + 196 = 200[/tex]
<=> [tex](4-x)^{2} = 4[/tex]
<=> (4-x) = 2 or (4-x) = -2
<=> x = 2 or x = 6
=> the sum of all possible values of x is: 2+6 = 8
