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Let line t be the line represented by x - 2y = 7and let line p be the line perpendicular to line t and containing the point (4,-4). What is the x-coordinate of the point common to line t and line p? Express your answer as a common fraction.

 Nov 17, 2020
 #1
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x - 2y  =7  →    2y  = x - 7    →  y = (1/2)x - 7/2   the slope of  t  =  (1/2)

 

The slope of a line perpendicuar to this   = -2

 

And it contains the point ( 4, -4)

 

Equation of p

 

y = -2(x - 4)  -4

y = -2x + 8 - 4

y = -2x + 4

 

x intersectionof these lines

 

(1/2) x  - 7/2 =  -2x + 4

 

2x + (1/2) x  = 4 + 7/2

 

(4/2)x + ( 1/2) x  = 8/2 + 7/2

 

(5/2) x  = 15/2        

 

x  = (15/2) ( 2/5)   =  30/10   = 3

 

 

See the graph, here :  https://www.desmos.com/calculator/s0denwkyj8

 

 

cool cool cool

 Nov 17, 2020

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