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Sagot :
Answer:
y = - 1
Explanation:
Two lines are perpendicular if the product of their slopes is equal to -1.
Additionally, we can calculate the slope of a line with two points (x1, y1) and (x2, y2) as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace (x1, y1) by P(6, -2) and (x2, y2) by O(-2, 8), we get that the slope of PO is equal to:
[tex]m=\frac{8-(-2)}{-2-6}=\frac{8+2}{-8}=\frac{10}{-8}=-1.25[/tex]In the same way, if we replace (x1, y1) by (-4, 3) and (x2, y2) by (-9, y), we get that the slope of RS is equal to:
[tex]m_{}=\frac{y-3}{-9-(-4)}=\frac{y-3}{-9+4}=\frac{y-3}{-5}[/tex]Then, the product of these two slopes should be equal to -1, so we can write the following equation:
[tex]-1.25\cdot(\frac{y-3}{-5})=-1[/tex]So, solving for y, we get:
[tex]\begin{gathered} (-5)(-1.25)\cdot(\frac{y-3}{-5})=(-5)(-1) \\ -1.25(y-3)=5 \\ y-3=\frac{5}{-1.25} \\ y-3=-4 \\ y=-4+3 \\ y=-1 \end{gathered}[/tex]Therefore, the value of y is equal to -1
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