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 $y$?

tomtom Aug 27, 2023

#1**+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

CPhill Aug 27, 2023