Question

The distance between the two points is 20. If the location of the points is at (11, 1) and (x, 17).

What are the possible values of x?

Answer 1

Given:

The distance between the two points (11, 1) and (x, 17) is 20.

To find:

The possible values of x.

Solution:

Distance formula is:

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using this formula, the distance between (11, 1) and (x, 17) is

`D=√((x-11)^2+(17-1)^2)`

`20=√(x^2-22x+121+(16)^2)`

`20=√(x^2-22x+121+256)`

Taking square on both sides.

`400=x^2-22x+377`

`0=x^2-22x+377-400`

`x^2-22x-23=0`

Splitting the middle term, we get

`x^2-23x+x-23=0`

`x(x-23)+(x-23)=0`

`(x-23)(x+1)=0`

Using zero product property, we get

`x=-1,23`

Therefore, the possible values of x are -1 and 23.