Thread: altitude vertex A in coordinates

Okay so I have to find the length of an altitude from vertex A of triangle ABC

Co-ordinates: A(3,4) B (4,-3) C (-4,-1)

Slope of CB= -1/4
Slope of Altitude= 4

Equations of the lines: CB y=-1/4x-2
Altitude A y=4x-8

Okay I think this is where I go wrong. I am suppose to find the length of the altitude from vertex A so I assume I must find the P.O.I. My answers for that are formed from using substitution:

x= 24/17 y=-40/17

Now to find the distance I use length= Squere Root((X2-X1)^2+(Y2-Y1)^2)

The answer in my book says 6.55 units while I get approx. 9.12 units.

My question where I am I going wrong? (or is the book wrong...its known for being wrong )

Hello, Tuesday's Gone!

Your work is correct ... up to finding the length.

You found that the foot of the altitude is: .D:(24/17, -40/17) . Right!

The answer in my book says 6.55 units while I get approx. 9.12 units.

Sorry, the book is right.

The distance from D:(24/17,-40/17) to A:(3,4) is:
. . . . . . . . _______________________
. . d . = . √(3 - 24/17)² + (4 + 40/17)² . = . 6.548461876 . ≈ . 6.55