Question

a line segment is of length 5 cm if the coordinates of its one end are (2,2) and that of the other end are(-1,x) then find the value of x

Answer 1

A line segment is of length 10 units, if the coordinates of its one end are (2,-3) and the abscissa of the other end is 10, then its ordinate 

Answer 2

Answer:

The possible values of x are -2 and 6.

Step-by-step explanation:

It is given that length of a line segment is 5 cm.

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The coordinates of its one end are (2,2) and that of the other end are (-1,x).

Using distance formula, the distance between (2,2) and (-1,x) is

$d=\sqrt{(-1-2)^2+(x-2)^2}$

$d=\sqrt{(-3)^2+x^2-4x+4}$

$d=\sqrt{9+x^2-4x+4}$

$d=\sqrt{x^2-4x+13}$

Substitute d=5 in the above equation.

$5=\sqrt{x^2-4x+13}$

Taking square both sides.

$25=x^2-4x+13$

$-=x^2-4x+13-25$

$0=x^2-4x-12$

Splitting the middle term, we get

$0=x^2-6x+2x-12$

$0=x(x-6)+2(x-6)$

$0=(x+2)(x-6)$

Using zero product property we get

$x+2=0\Rightarrow x=-2$

$x-6=0\Rightarrow x=6$

Therefore the possible values of x are -2 and 6.