Question

The lines shown below are perpendicular.

5
(-2,4)
4
(2.1)
5
(0,-2)
(-4,-2)
A. True
B. False

Answer 1

False. The two lines in this diagram are not perpendicular with one another.

Explanation:

Two lines in a plane are perpendicular if and only the product of their slopes is
`(-1)`.

If a non-vertical line in a plane goes through two points,
`(x_(0),\, y_(0))` and
`(x_(1),\, y_(1))` (
`x_(0) \\e y_(0)`,) the slope of this line would be:

`\begin{aligned}m &= (y_(0) - y_(1))/(x_(0) - x_(1))\end{aligned}`.

Find the slope of the two lines given the coordinates of the points.

Slope of the line sloping downwards:

`\begin{aligned}m_(a) &= (4 - (-2))/((-2) - 0) \\ &= (6)/((-2)) \\ &= (-3)\end{aligned}`.

Slope of the line sloping upwards:

`\begin{aligned}m_(b) &= (1 - (-2))/(2 - (-4)) \\ &= (3)/(6) \\ &= (1)/(2)\end{aligned}`.

The product of the slopes of the two lines is:

`\begin{aligned}m_(a)\, m_(b) &= (-3) * (1)/(2) \\ &= \left(-(3)/(2)\right)\end{aligned}`.

Therefore, these two lines are not perpendicular to one another since the product of their slopes isn't
`(-1)`.