Question

Line / has a slope of. The line through which of the following pair of points is

perpendicular to /?
A. (4, 6), (2, 2) B. (8,8), (2, 4)
C. (8,2), (2,4)
D. (6,2), (2, 4)

Answer 1

The slope of a line.

Let
`A(x_A,\ y_A),\ B(x_B,\ y_B)`. Then a slope of the line AB represent the formula:

`m=(y_B-y_A)/(x_B-x_A)`

Substitute the coordinate od the points to the formula of a slope.

`A.\\(4,\ 6),\ (2,\ 2)\\\\m=(2-6)/(2-4)=(-4)/(-2)\\\\\huge\boxed{m=2}`

`B.\\(8,\ 8),\ (2,\ 4)\\\\m=(4-8)/(2-8)=(-4)/(-6)\\\\\huge\boxed{m=(2)/(3)}`

`C.\\(8,\ 2),\ (2,\ 4)\\\\m=(4-2)/(2-8)=(2)/(-6)\\\\\huge\boxed{m=-(1)/(3)}`

`D.\\(6,\ 2),\ (2,\ 4)\\\\m=(4-2)/(2-6)=(2)/(-4)\\\\\huge\boxed{m=-(1)/(2)}`