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 1

Answer: x = 3, 19

Explanation:

Given

Two points i.e.
`(11,2)\ \text{and}\ (x,-4)` are given

Distance between them is 10 units

Distance is given by the distance formula

`\Rightarrow d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Distance between two points is

`\Rightarrow 10=√((x-11)^2+(-4-2)^2)`

Squaring both sides

`\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`

i.e.
`x\ \text{can be }\ x=3\ or\ 19`