Question

The distance between the points (x,7) and (-1,6) is equal to the distance between the points (4,5) and (-3,4) . The possible values of x are?

Answer 1

The value of x is either +6 or -8

Step-by-step explanation:

Given: Two couple of points

To find: the value of x

Distance between (x,7) and (-1,6)= $\sqrt{[x-(-1)]^{2} +[7-6]^{2} }$  =$\sqrt{(x+1)^{2}+1 }$

Distance between (4,5) and (-3,4)=$\sqrt{[4-(-3)]^{2} +[5-4]^{2} }$  =$\sqrt{49+1}$ =$\sqrt{50}$

According to the question, the distances are equal

So $\sqrt{(x+1)^{2}+1 }$ = $\sqrt{50}$

=>(x+1)^2 + 1 =50

=> (x+1)^2 =49

=> x+1 =+7, -7

=>x =6, -8