Answer: x = 3, 19
Step-by-step explanation:
Given
Two points i.e. [tex](11,2)\ \text{and}\ (x,-4)[/tex] are given
Distance between them is 10 units
Distance is given by the distance formula
[tex]\Rightarrow d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Distance between two points is
[tex]\Rightarrow 10=\sqrt{(x-11)^2+(-4-2)^2}[/tex]
Squaring both sides
[tex]\Rightarrow 100=(x-11)^2+(-6)^2\\\Rightarrow 100=x^2+121-22x+36\\\Rightarrow x^2-22x+57=0\\\Rightarrow x^2-19x-3x+57=0\\\Rightarrow x(x-19)-3(x-19)=0\\\Rightarrow (x-19)(x-3)=0[/tex]
i.e. [tex]x\ \text{can be }\ x=3\ or\ 19[/tex]
