Question

If A = (x, -7), B=(2, 5) and AB = 13 units, find x

Answer 1

Given:

Coordinates A and B are given to which are A=(x,-7),B=(2,5),also AB=13

To Find:

The value of x?

Step-by-step explanation:

• we have Coordinates A and B are given to which are A=(x,-7),B=(2,5)

• We know distance of AB is given by formula which is

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

       Where  A= (x,-7)=($x_1,y_1$),B=(2,5)=($x_2,y_2$)

• Thus distance of AB will be

                      [tex]Distance =\sqrt{(2-x)^2+(5+7)^2} \\\\ 13=\sqrt{(x^2+4-4x)+144} \\\\ 13^2=169=x^2-4x+148\\\\ x^2-4x-21=0[/tex]

• Now factorize the above equation to get solution

                     [tex]x^2-4x-21=0\\\\ x^2-7x+3x-21=0\\\\ x(x-7)+3(x-7)=0\\\\ (x-7)(x+3)=0\\\\ x=7,x=-3[/tex]

Thus we get value of x can be either 7 or -3.