The square of the distance between two points is the sum of the squares of the difference between two coordinates. The value of n can be -13 or 3.
What is the distance between two points?
The distance between two points is given by the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
As it is given that the distance between points R and S is half the distance between points S and T.
[tex]2(RS) = ST[/tex]
Now, the distance between RS can be written as,
[tex]RS=\sqrt{[-6-(-2)]^2+[-5-(-5)]^2}\\RS = \sqrt{(-6+2)^2+(0)^2}\\RS = \sqrt{16}\\RS = \pm 4[/tex]
Further, we can write,
[tex]2(RS) = ST\\\\2(\pm 4) = \sqrt{[-2-(-2)]^2+[-5-n]^2}\\\\\pm 8 = \sqrt{(0)^2+(-5-n)^2}\\\\\pm 8^2=(-5-n)^2\\\\\pm8=(-5-n)\\\\[/tex]
When the value of 8 is positive,
[tex]+8+5=-n\\\\13=-n\\\\n=-13[/tex]
When the value of 8 is negative,
[tex]-8+5=-n\\\\-3=-n\\\\n=3[/tex]
Hence, the value of n can be -13 or 3.
Learn more about the Distance between two points:
https://brainly.com/question/16410393
#SPJ1
