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avatar+1467 

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 $y$?

 Aug 27, 2023
 #1
avatar+126653 
+1

We can find an equation of the  line through B and  C

The slope of this line is  [ 2 - - 8 ] / [ -3 -1 ] =  10  / -4 =  -5/2

The equation of  the line through A will have a negative reciprocal slope =  2/5

 

So.....the equation of this  line is

 

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

y = (2/5)x - 4/5 + 3

y = (2/5)x +11/5

 

When x =  0  ,  y =  11/5  =  2.2

 

cool cool cool

 Aug 27, 2023

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