Question Given (11,2) and (x,−4), find all x such that the distance between these two points is 10. Separate multiple answers with a comma.

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] Log in to Reply

Answer: x = 3, 19Step-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]