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# Need help with this coordinate question.

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Hi there everyone!  I'm stuck on question 2c (find the exact x coordinate of E).  Please help, thanks. Oct 21, 2019

#1
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First, find the slope of  AD   = [ 7 - 2 ]           5             5

_______  =   -----  =    - ___

[ 1 - 8]          -7             7

The slope of  a perpendicular line to this  =  7

__

5

So....using D  and  this slope we have that

y = (7/5) ( x - 8)  + 2         multiply through by  5

5y  = 7 (x - 8) + 10

5y =  7x  -  56  +  10

5y =  7x   - 46

-7x + 5y  =  -46     multiply  through by   -1

7x   -   5y   =   46      (1)

This line will intersect AB

The equation of  AB  is  y   = 7

Sub   y = 7   into (1)   and we have that

7x  - 5(7)   = 46

7x  -  35  =  46       add   35 to both sides

7x  =  81        divide both sides by  7

x  =  81/7 =  x coordinate of E

So

E  = (81/7, 7)   Oct 21, 2019
#2
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Thank you so much!  It was finding the equation of AB that got me confused on this question.   Much appreciated.

Umbrella  Oct 21, 2019
#3
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OK....you're welcome   !!!   CPhill  Oct 21, 2019