Question

find the value of x for which the distance between points A(x, 7) and B(-2,3) is 4√5 units.
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Answer 1

Answer:

either x=6 or x=-10

Step-by-step explanation:

check out the solution in the photo

Answer 2

Given,

                A= (x,7) = (x₁ ,y₁)

                B=(-2,3) = (x₂ ,y₂)

                distance between A and B= AB= 4√5

To find,

               Value of x

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

We know that,

By distance formula;

∴ Distance between two points = $\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }$

                                      ⇒  4$\sqrt{5}$ = $\sqrt{(-2-x)^2+(3-7)^2}$ (squaring both sides)

                                      ⇒ $16*5 = (-2-x)^2 +(-4)^2$

                                      ⇒ $80= 4+x^2+4x+16$

                                      ⇒ $x^2+4x-60=0$

                                      ⇒ $x^2+10x-6x-60=0$  (Factorizing the quadratic)

                                      ⇒ $x(x+10)-6(x+10)=0$

                                      ⇒ $(x+10)(x-6)=0$

                                      ⇒ $x = -10, 6$

Thus, the two values of x are -10 and 6.

(You must note that there are two values of x because of the quadratic equation formed by applying the distance formula.)