Question

.If the distance between the points P(2,-3) and Q(x,-9) is 85 units., then find

the values of x.​

Answer 1

 Correct QUESTION-:

If the distance between the points P(2,-3) and Q(x,-9) is  $\bf\; \sqrt{85}$  units., then find

the values of x.​

EXPLANATION-:

The distance between two point ,(x₁,y₁) and (x₂,y₂) is given by the formula-:

$\rightarrow \boxed{\bf\; d=\sqrt{(x_{2}-x_{1} )^2 +(\sqrt{y_{2}-y_{1})^2} }}$

Here-:

• x₁= x
• x₂=2
• y₁=-9
• y₂=-3

Putting values in the formula-:

$\rightarrow \bf\; \sqrt{85} =\sqrt{(x-2)^2+(-9+3)^2} \\\\\rightarrow \bf\; 85=(x-2)^2+36 \qquad \qquad \qquad \{Squaring\;both\;sides \}\\\\\rightarrow \bf\; 49=(x-2)^2\\\\\rightarrow \bf\; \boxed{\bf\; x=9,-5}$

∴The value of x is 9 or -5 .