Answer:
A. -1
Step-by-sep explanation:
If PQ is perpendicular to RS, therefore, the slope of RS would be the negative reciprocal of PQ.
Slope of PQ:
P(6,-2), Q(-2, 8)
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 -(-2)}{-2 - 6} = \frac{10}{-8} = -\frac{5}{4} [/tex]
Slope of RS:
Slope of RS is the reciprocal of the slope of PQ, since they are perpendicular.
⅘ is the reciprocal of -⁵/4. Therefore, the slope of RS = ⅘.
Use the slope formula to find the value of y in R(-4, 3), S(-9, y).
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Plug in the value
[tex] \frac{4}{5} = \frac{y - 3}{-9 -(-4)} [/tex]
[tex] \frac{4}{5} = \frac{y - 3}{-5} [/tex]
Cross multiply
[tex] (4)(-5) = (y - 3)(5) [/tex]
[tex] -20 = 5y - 15 [/tex]
Add 15 to both sides
[tex] -20 + 15 = 5y - 15 + 15 [/tex]
[tex] -5 = 5y [/tex]
Divide both sides by 5
[tex] \frac{-5}{5} = \frac{5y}{5} [/tex]
[tex] -1 = y [/tex]
y = -1
