Answer:
E. -1/2
Step-by-step explanation:
When two lines are said to be perpendicular to each other, the slope of one is the negative reciprocal of the other.
Therefore, given that [tex] \frac{x - 1}{4} [/tex] is the slope of [tex] \overline{QR} [/tex], and ⁸/3 is the slope of [tex] \overline{ST} [/tex], if both lines are perpendicular, it means that the slope of [tex] \overline{ST} [/tex] would be the negative reciprocal of the slope of [tex] \overline{QR} [/tex].
Therefore:
[tex] \frac{x - 1}{4} = -\frac{3}{8} [/tex]
Cross multiply
[tex] (x - 1)(8) = (-3)(4) [/tex]
[tex] 8x - 8 = -12 [/tex]
Add 8 to both sides
[tex] 8x = -12 + 8 [/tex]
[tex] 8x = -4 [/tex]
Divide both sides by 8
[tex] x = \frac{-4}{8} [/tex]
[tex] x = \frac{-1}{2} [/tex]
