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If line m is perpendicular to line l and line l passes through points

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
If line m is perpendicular to line l and line l passes through points  [#permalink]

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05 Sep 2018, 23:38
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Difficulty:

45% (medium)

Question Stats:

53% (01:01) correct 47% (01:05) wrong based on 57 sessions

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If line m is perpendicular to line l and line l passes through points (6, 5) and (6, 8), what is the slope of line m?

A. -1
B. 0
C. 1
D. the slope is undefined
E. the slope cannot be determined from the information given

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Director
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
Re: If line m is perpendicular to line l and line l passes through points  [#permalink]

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06 Sep 2018, 00:19
Bunuel wrote:
If line m is perpendicular to line l and line l passes through points (6, 5) and (6, 8), what is the slope of line m?

A. -1
B. 0
C. 1
D. the slope is undefined
E. the slope cannot be determined from the information given

slope of line l =$$\frac{y2-y1}{x2-x1}$$ = 3/0 (undefined )
since line l and m are perpendicular
slope of l * slope of m = -1
slope of m = $$\frac{-1}{(3/0)}$$= 0
Senior SC Moderator
Joined: 22 May 2016
Posts: 2491
Re: If line m is perpendicular to line l and line l passes through points  [#permalink]

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07 Sep 2018, 12:35
Bunuel wrote:
If line m is perpendicular to line l and line l passes through points (6, 5) and (6, 8), what is the slope of line m?

A. -1
B. 0
C. 1
D. the slope is undefined
E. the slope cannot be determined from the information given

Solution
Line $$l$$ is vertical.
Slope of line $$l$$: $$\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{8-6}{5-5}=\frac{2}{0}$$
Any number divided by 0 is undefined.
Slope of line $$l$$: undefined

Line $$m$$ is perpendicular to line $$l$$
Generally, perpendicular lines have slopes that are negative reciprocals of one another. Not in this case.
We cannot calculate the negative reciprocal of an undefined number.

However, any horizontal line is perpendicular to any vertical line.
Line $$m$$ is horizontal; the slope of a horizontal line = 0
Draw a horizontal line, pick two points, and calculate slope (see notes below)
Slope of line $$m = 0$$

HOW TO REMEMBER WHICH LINE GETS WHICH SLOPE
To keep vertical and horizontal lines' slopes straight, use coordinates or a mnemonic

• Slope from coordinates
Line $$l$$: (6, 5) and (6, 8)
Line $$m$$: draw any horizontal line and pick two points.
From diagram, two points on Line $$m$$: (1, 2) and (3, 2)

Slope of line $$m$$: $$\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-2}{3-1}=\frac{0}{2}=0$$
Slope of line $$m=0$$

Slope of line $$l$$: $$\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{8-6}{5-5}=\frac{2}{0}$$
Any number divided by 0 is undefined. Slope of line $$l$$: undefined

• Use a mnemonic.
hOrizontal has a letter O
The letter O in hOrizontal looks like a zero, 0
A hOrizontal line has slope of 0
-- "Vertical," obviously, does not have the letter "O"

Other mnemonics
-- One very good site uses "neither positive nor negative number" and "no number that is both positive and negative." HERE
-- Another site uses the acronyms VUX and HOY , which are simple and effective, HERE

Attachment:

verthorzlines.jpg [ 43.33 KiB | Viewed 423 times ]

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Re: If line m is perpendicular to line l and line l passes through points   [#permalink] 07 Sep 2018, 12:35
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