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किसी त्रिभुज ABC के शीर्ष `(0,0) ,(1,-1)` तथा (3 ,2 ) है| इसके शीर्षो की सम्मुख भुजाओं से दूरियाँ ज्ञात कीजिए|

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माना `A-= A (0,0) ,B-= B (1,-1) ,C -=C (3,2)`
अब, BC का समीकरण
` " " y+ 1= (-1-2)/( 1-3) (x-1) `
`rArr" "y+1 =(3)/(2) (x-1)`
`rArr " "3x -2y -5=0 `
अब, ` " "AL ` की लम्बाई ` =A ` से BC पर डाले गये लम्ब की लम्बाई
` " " (| 0-0-5|)/(sqrt(9+4) )= (5)/(sqrt(3))`
तथा CA का समीकरण ltBrgt `" "y-2 =(2-0)/(3-0) (x-3) `
`rArr" "3y -6=2x -6 `
`rArr " " 2x- 3y =0`
तथा ` " "` शीर्षलम्ब `BM=B ` से रेखा AC पर डाले गये लम्ब की लम्बाई
` " "= (2(1)-3(-1))/(0-1)=(5)/(sqrt(13))`
इसी प्रकार AB का समीकरण
` " "y-0 =(0+1)/(0-1) (x-0)`
`rArr" "x+ y=0 `
तथा ` " "` शीर्षलम्ब CN =C से रेखा AB पर डाले गये लम्ब की लम्बाई
` " "= (3+2)/(sqrt(1+1))=(5)/(sqrt(2))`
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