Question

If A(2,-1),B(-4,2) and C(2,5) are the veertices of triangle ABC then find the length of altitude AD

Answer 1

Answer:

$x=\frac{-2}{5},y=\frac{19}{5}$ are the coordinates of D.

Step-by-step explanation:

We have been given a  triangle  with all its vertices A(2,-1) , B(-4,2) and C(2,5).

Please look at the attachment to see the triangle given.  

We need to find the coordinates of the D

So, we will find the slope of BC by two point form.

$\frac{y_2-y_1}{x_2-x_1}$

$\frac{5-2}{2+4}$

$\frac{3}{6}=\frac{1}{2}$

And slope of BC and AD will be in reciprocal because AD is normal to BC

Slope of AD=2

Now, we will find the equation of BC and Ad by slope point form.

Equation of BC $y-5=\frac{1}{2}(x-2)$

$y=\frac{x}{2}+4$     (1)

And equation of AD is:$y+1=(-2)(x-2)$

$\Rightarrow y=-2x+3$  (2)

Now, we will solve (1) and (2) for x and y to get the coordinates of D.

$x=\frac{-2}{5},y=\frac{19}{5}$ are the coordinates of D.