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Find the length of altitude through A of...

Find the length of altitude through `A` of the triangle `A B C ,` where `A-=(-3,0)B-=(4,-1),C-=(5,2)`

Text Solution

Verified by Experts

The correct Answer is:
`(22)/(sqrt10)`

In the figure , AL is altitude .
Area of triangle `=(1)/(2)[-3(-1-2)+4(2-0)+5(0+1)]=11`
Also, `BC=sqrt((5-4)^2+(2+1)^(2))=sqrt(1+9)=sqrt(10)`
Now, area of triangle `=(1)/(2)xxALxxBC`
`therefore AL=(2xx11)/(sqrt(10))=(22)/(sqrt(10))` .
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