Question

Line m contains the ordered pairs (11,-6) and (7,2). line p is perpendicular to line m and contains the ordered pairs (3,4) and (x,-2). what is the value of x

Answer 1

`x=-9`

Explanation:

Perpendicular lines means that their slopes are negative reciprocals of each other.

In other words, when you multiply the 2 slopes, that will gives us -1.

Slope's formula is m =
`(y_2-y_1)/(x_2-x_1)`

• Taking the first two points, we have:

`(y_2-y_1)/(x_2-x_1)\\=(2--6)/(7-11)\\=(8)/(-4)\\=-2`

• Taking the second two points, we have:

`(-2-4)/(x-3)\\=(-6)/(x-3)`

Now multiplying these 2 expressions and equating it to -1, we can solve for x:

`-2*(-6)/(x-3)=-1\\(12)/(x-3)=-1\\12=-1(x-3)\\12=-x+3\\x=3-12\\x=-9`

x = -9