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A line with slope equal to 1 and a line with slope equal to 3 intersect at the point P(1,6)  What is the area of triangle PQR?

 

 Jun 25, 2021
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QP  must lie on  the line with a slope of 1

Call  Q  =   (x1 , 0)

 

So

 

(6 - 0 )  / ( 1  - x1)  =  1

6   =   1 - x1

x1  = 1 - 6

x1 =  -5

So  Q  =(  -5,0)

 

Likewiae  RP  must lie on the line with a slope of 3

Call R  =  (x2 , 0)

 

So

(6-0) / (1 - x2)  =  3

6 =  3 ( 1 - x2)

2  = 1 - x^2

x2 =  1 - 2

x2 =  -1

So R  =(  -1, 0)

 

So   QR =  4=  base of PQR

And the  height of  the  triangle  =  6

 

Area =   (6 * 4)   /  2   =    12

 

cool cool cool

 Jun 25, 2021

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