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

y = - 1

Step-by-step 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=(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=(8-(-2))/(-2-6)=(8+2)/(-8)=(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_{}=(y-3)/(-9-(-4))=(y-3)/(-9+4)=(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((y-3)/(-5))=-1`

So, solving for y, we get:

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

Therefore, the value of y is equal to -1