In the standard (x, y) coordinate plane, if a line L is perpendicular to the line passing … — ACT

In the standard $(x, y)$ coordinate plane, if a line $L$ is perpendicular to the line passing through the points $(2, 5)$ and $(2, -3)$ , then the slope of line $L$ is $0$ .

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Cevap

The statement is true because the line passing through the points

(2, 5)

and

(2, -3)

is vertical, and any line perpendicular to a vertical line is horizontal, which has a slope of

0

The line passing through

(2, 5)

and

(2, -3)

has identical x-coordinates, which defines a vertical line. Any line perpendicular to a vertical line is horizontal, and horizontal lines have a slope of

0

Adım Adım Çözüm

Identify the orientation of the line passing through the points

(2, 5)

and

(2, -3)

Since both coordinates share the same x-value (

x = 2

), the line is vertical.

In the standard coordinate plane, a line connecting points with identical x-coordinates is vertical and has an undefined slope.

Determine the orientation of line

L

, which is perpendicular to this vertical line.

Line

L

must be a horizontal line.

By geometric definition, a line perpendicular to a vertical line in the coordinate plane is horizontal.

Determine the slope of the horizontal line

L

The slope of line

L

0

A horizontal line has no vertical change (rise =

0

) as the horizontal position changes, resulting in a slope of

0

Anahtar Kavram

The relationship between vertical and horizontal lines in the coordinate plane, specifically that perpendicular lines to vertical lines are horizontal and have a slope of

0

Alternatif Yöntem

Write the equation of the line passing through

(2, 5)

and

(2, -3)

, which is

x = 2

. Any line perpendicular to

x = 2

must be in the form

y = c

where

c

is a constant. The slope of any line in the form

y = c

0

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Soru

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Alternatif Yöntem

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