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Triangle $ABC$ has vertices $A(2, 3),$ $B(1, -8)$ and $C(-3, 2).$ The line containing the altitude through $A$ intersects the point $(0, y).$ What is the value of $y$?

 Feb 15, 2024
 #1
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BC  has the slope   [ -8 - 2 ] / [ 1 - - 3] = -10 / 4  = -5/2

 

The altitude through A will have the slope (2/5)

Writing an equation for  a line containg  this  altitude, we have

 

y =(2/5) (x - 2) + 3

 

When x   = 0,  y =  (2/5)(0 -2) + 3 =  -4/5 + 3 =  11/5 = 2.2

 

cool cool cool

 Feb 16, 2024

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