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

Answer:

$x=-9$

Step-by-step 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 = $\frac{y_2-y_1}{x_2-x_1}$

• Taking the first two points, we have:

$\frac{y_2-y_1}{x_2-x_1}\\=\frac{2--6}{7-11}\\=\frac{8}{-4}\\=-2$

• Taking the second two points, we have:

$\frac{-2-4}{x-3}\\=\frac{-6}{x-3}$

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

$-2*\frac{-6}{x-3}=-1\\\frac{12}{x-3}=-1\\12=-1(x-3)\\12=-x+3\\x=3-12\\x=-9$

x = -9