On a coordinate plane, 2 lines are shown. Line P Q has points (negative 8, 2) and (4, 2). Line M N has points (8, 6) and (8, neg

Question

6 days ago

9

ative 8). What is the slope of line PQ? What is the slope of line MN? How are the two lines related?

2 answers:

lawyer [4K] · Answer 1 · 2026-02-27T01:02:15+03:00

Response

The coordinates for line PQ are (-8,2) and (4,2)

The slope of this line is

$m_1 = \frac{y_2-y_1}{x_2-x_1}$

$m_1 = \frac{2-2}{4+8}$

$m_1 = 0$

Coordinates for line MN are (8,-6) and (8,-8)

The slope of this line is

$m_2 = \frac{y_2-y_1}{x_2-x_1}$

$m_2 = \frac{2-2}{4+8}$

Line PQ runs parallel to the x-axis, intersecting at y = 2.

Line MN runs parallel to the y-axis, intersecting at x = 8.

Both lines intersect at the point (8,2).

Svet_ta [4.3K] · Answer 2 · 2026-02-27T01:03:04+03:00

Response:

PQ's slope is 0

MN's slope equals infinity

The lines PQ and MN are perpendicular to one another

Detailed explanation:

For two points in the coordinate plane, denoted as (x1, y1) and (x2, y2), the slope is determined as follows:

$y1 - y2/x1-x2\\\\For \ line \ PQ\\slope = 2 - 2/-8-4 = 0\\\\For \ line \ MN \\slope = 6 - (-8)/8-8 = 1/0 = infinity\\\\$

If a line has a slope of zero, it runs parallel to the X-axis and stands perpendicular to the Y-axis

If a line's slope is infinite, it is parallel to the Y-axis and perpendicular to the X-axis

Moreover, it is established that X and Y are perpendicular to each other.

As PQ's slope is zero, it runs parallel to the X-axis and perpendicular to the Y-axis

With MN having an infinite slope, it runs parallel to the Y-axis and perpendicular to the X-axis.

Therefore, lines PQ and MN are indeed perpendicular.