+0  
 
0
35
1
avatar+324 

A is the point (-3, 6). Let (𝑥, 𝑦) be any point on the line 𝑦 = 2𝑥.

a) Write an equation in terms of 𝑥 for the distance between (𝑥, 𝑦) and A(-3, 6).

b) Find the coordinates of the two points, B and C, on the line 𝑦 = 2𝑥 and which are a distance of 6 from (-3, 6).

c) Find the equation of 𝑙1 that is perpendicular to 𝑦 = 2𝑥 and goes through the point (-3, 6) in the form 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0, 𝑤ℎ𝑒𝑟𝑒 𝑎, 𝑏 𝑎𝑛𝑑 𝑐 𝑎𝑟𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟𝑠.

please explain each steps thanks!!!!

YEEEEEET  Oct 29, 2018
edited by YEEEEEET  Oct 29, 2018
 #1
avatar+90995 
+1

A is the point (-3, 6). Let (𝑥, 𝑦) be any point on the line 𝑦 = 2𝑥.

a) Write an equation in terms of 𝑥 for the distance between (𝑥, 𝑦) and A(-3, 6).

b) Find the coordinates of the two points, B and C, on the line 𝑦 = 2𝑥 and which are a distance of 6 from (-3, 6).

c) Find the equation of 𝑙1 that is perpendicular to 𝑦 = 2𝑥 and goes through the point (-3, 6) in the form 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0, 𝑤ℎ𝑒𝑟𝑒 𝑎, 𝑏 𝑎𝑛𝑑 𝑐 𝑎𝑟𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟𝑠.

please explain each steps thanks!!!!

 

a)

distance  = sqrt  [ ( x + 3)^2  + ( y - 6)^2]

 

b)

Let  y   = 2x  and we want to solve this

 

6  = sqrt [ ( x + 3)^2  + (2x - 6)^2 ]     square both sides

 

36  =  ( x + 6x + 9)  + ( 4x^2 - 24x + 36 )   simplify

 

36  = 5x^2 - 18x + 45    rearrange as

 

5x^2  - 18x  + 9  = 0        factor

 

(5x - 3) ( x  - 3)   = 0

 

Set both factors to 0  and solve for x and we get that

 

x  = 3/5  or   x  =  3

 

And the associated y coordinates are  y  = 2(3/5)  = 6/5

And   y  = 2(3)  =  6

 

So...the two points are    ( 3/5, 6/5)   and  ( 3, 6)

 

 

c )  Perpendicular to y  = 2x   and  passing through (-3, 6)

The slope of this line is   (-1/2)

So....the equation is

 

y  = (-1/2) ( x + 3) + 6

y = (-1/2)x - 3/2 + 12/2

y = (-1/2)x + 9/2

 

 

cool cool cool

CPhill  Oct 29, 2018

21 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.