Question

If P(6,-2). O(-2,8), R(-4, 3), and S(-9, y). find the value of y so that PO perpendicular to RS.please?

Answer 1

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

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:

$m=\frac{8-(-2)}{-2-6}=\frac{8+2}{-8}=\frac{10}{-8}=-1.25$

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:

$m_{}=\frac{y-3}{-9-(-4)}=\frac{y-3}{-9+4}=\frac{y-3}{-5}$

Then, the product of these two slopes should be equal to -1, so we can write the following equation:

$-1.25\cdot(\frac{y-3}{-5})=-1$

So, solving for y, we get:

$\begin{gathered} (-5)(-1.25)\cdot(\frac{y-3}{-5})=(-5)(-1) \\ -1.25(y-3)=5 \\ y-3=\frac{5}{-1.25} \\ y-3=-4 \\ y=-4+3 \\ y=-1 \end{gathered}$

Therefore, the value of y is equal to -1