Question 22: Perpendicular to the line

Algebra Level 2

MA.912.A.3.10 - Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.

Algebra 1 EOC Study Guide. How many can you solve correctly?

B D A C

10 solutions

Lew Sterling Jr
Jan 12, 2015

Question and your solution have very small font, it may be difficult to read them.

Would you mind re-editing them so that the fonts are a bit larger? That would help you acquire more audience for this problem.

Soumo Mukherjee - 6 years, 5 months ago

Tried that; nothing. Right click the picture and open it to a new tab.

Lew Sterling Jr - 6 years, 5 months ago

Ok, there's that way too.

You can try this and lets see if it works or not. First select 'toggle latex' by clicking on your profile picture (i.e top right corner), then copy the following text and paste it in your problem area:

$22.$ Which equation represents the line passing through the point $\left( 4,-16 \right)$ and is perpendicular to the line $y=-\cfrac { 2 }{ 3 } x+8 ?$

$A.\quad y=\cfrac { 2 }{ 3 } x-22\\ B.\quad y=-\cfrac { 2 }{ 3 } x-22\\ C.\quad y=-\cfrac { 3 }{ 2 } x-22\\ D.\quad y=\cfrac { 3 }{ 2 } x-22$

Soumo Mukherjee - 6 years, 5 months ago

Soumo Mukherjee
Jan 12, 2015

Our given line is $3y+2x-8=0$ . Any line $\bot$ to the given line will be of the form $2y-3x+\lambda =0$ , where $\lambda$ is any arbitrary constant. Since this line also passes through $\left( 4,-16 \right)$ , therefore we have $2\times (-16)-3\times 4+\lambda =0$ , which gives the value of $\lambda =44$ . So the sought out line is completely defined and its equation is $2y-3x+44=0$ which on further transformation becomes $y=\cfrac { 3 }{ 2 } x-22$ . Hence the answer.

Last step gives you (...) - 22, not - 44.

Roberto Villadangos Carrera - 6 years, 5 months ago

yup... thanks for pointing.

Soumo Mukherjee - 6 years, 5 months ago

Saaket Sharma
Feb 26, 2015

In this problem we don't even need to check whether the line passes through (4,-16).We know that product of slopes of two perpendicular lines is -1. And only option D corresponds to this condition. (-2/3)*(3/2)=-1..

Aman Jain
Feb 14, 2015

Interchange the co-officiants of x and y and also signs of them as compared to given equation and than pass them through given points to get constant term.

U.N. Owen
Jan 25, 2015

Since perpendicular lines have opposite slopes, a slope of -2/3 in the original line will be a slope of 3/2 in the perpendicular.

Every option has b = - 22, so no more work is actually necessary.

D) y = 3/2 x -22

Rithvik Gundlapalli
Jan 22, 2015

You don't even have to solve anything. If you know that the slope of a perpendicular line is the negative reciprocal of the original line, then there is only one choice (D) which contains the correct slope.

Karem Cortés Ruiz
Jan 21, 2015

A perpendicular line has a reciprocal inverse (I'm not sure of its name in English, in Spanish is called "recíproco opuesto") in its slope. Lets remember: y=mx+b, m is the slop, which means:
number of slope = m
reciprocal inverse of slope = -1/m

so if the slope is 3/2, its reciprocal inverse is -2/3. The only choice with this slope is D :)

Lu Chee Ket
Jan 20, 2015

Based on Tan (A - B) = (Tan A - Tan B)/ (1 + Tan A Tan B) derived from Sin (A - B) = Sin A Cos B - Cos A Sin B and Cos (A - B) = Cos A Cos B + Sin A Sin B which again derived by drawing an acute triangle,

Tan (90 d) meant for 1 + Tan A Tan B = 0.

1 + m1 m2 = 0 => m2 = -1/ m1

Substitutes (4, -16) into y = (3/ 2) x - 22 which can be found correct, it is the answer.

Mohd Zain
Jan 16, 2015

Perpendicular line hase opposite slope.so slope =3/2. now,(y-y1)=m(x-x1).x=4,y=-16. y+16=3/2 (x-4). Y=3/2x-4-16. y=3/2x-22.

Kshitij Johary
Jan 14, 2015

Only the fourth line (option D) passes through the point (4,-16). Plugin the values and verify.

Only the fourth line has the correct gradient to be perpendicular - faster to check.

Chris Brooking - 6 years, 5 months ago

Question 22: Perpendicular to the line

10 solutions

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