SOLUTION: 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 $y$?

Question 1203459: 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 $y$?
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Triangle ABC has vertices A(2, 3), B(1, -8) and C(-3, 2).
The line containing the altitude is perpendicular to the line containing B(, ) and C(, )
find a slope of that line:

The line containing the altitude is perpendicular, so slope will be
then, using point slope formula , the line containing the altitude will be

the point A(, ) and

then
the point P(, ) will be

the point (, )

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Answer: y = 11/5 = 2.2

Explanation

Compute the slope of line BC

The slope of -5/2 means "go down 5 units every time we go 2 units to the right".
In short: "down 5, right 2".

The negative reciprocal slope will have us do two things:
flip the fraction
flip the sign

-5/2 becomes 2/5

The altitude line through point A has a slope of 2/5
Apply point-slope form

Plug in perpendicular slope

Plug in coordinates of point A

This is the equation of the altitude through point A. It is perpendicular to side BC.

Plug in x = 0 to find that y = 11/5 = 2.2 which is the final answer.

Here's the diagram

The blue line is the altitude through point A.
It intersects the y axis at (0, 11/5) = (0,2.2) which is marked as point D.

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