Question

Let A (-1, 1), B (5, 2) and c (3, -1) form the vertices of a triangle. Find the length of the altitude from A to BC.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

We want to find AD.
If we know the equation of BC, we can find AD using distance formula.

(1) Finding the equation of BC
$y-2=(x-5)\times \frac{-1-2}{3-5}$
$y-2=\frac{3}{2}(x-5)$
2y-4=3x-15
3x-2y-11=0

(2) Calculating AD using distance formula.
$AD=|\frac{3\times -1-2\times 1-11}{\sqrt{3^2+2^2}}|$
$=|\frac{-3-2-11}{\sqrt{1}3}|$
$=\frac{16}{\sqrt{13}}$