Answer:
Therefore,
[tex]x = 9[/tex]
Step-by-step explanation:
Given:
Let,
point L( x₁ , y₁) ≡ ( -6 , 2)
point M( x₂ , y₂ )≡ (x , 2)
l(AB) = 15 units (distance between points L and M)
To Find:
x = ?
Solution:
Distance formula between Two points is given as
[tex]l(LM)^{2} = (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}[/tex]
Substituting the values we get
[tex]15^{2}=(x--6)^{2}+(2-2)^{2}\\\\225=(x+6)^{2}[/tex]
Square Rooting we get
[tex](x+6)=\pm \sqrt{225}=\pm 15\\\\x+6 = 15\ or\ x+6 = -15\\\\x= 9\ or\ x = -21[/tex]
As point M is located in the first quadrant
x coordinate and y coordinate are positive
So x = -21 DISCARDED
Hence,
[tex]x = 9[/tex]
Therefore,
[tex]x = 9[/tex]
