SOLUTION: From the point p(-2,4),if PQ is drawn perpendicular to the line 7x-24y+10=0,find the equation of line PQ and its length.

Algebra ->  Length-and-distance -> SOLUTION: From the point p(-2,4),if PQ is drawn perpendicular to the line 7x-24y+10=0,find the equation of line PQ and its length.      Log On


   

Question 989992: From the point p(-2,4),if PQ is drawn perpendicular to the line 7x-24y+10=0,find the equation of line PQ and its length.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Write given equation in slope-intercept form
+7x+-+24y+%2B+10+=+0+
+24y+=+7x+%2B+10+
+y+=+%287%2F24%29%2Ax+%2B+5%2F12+
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Any line perpendicular to this line will
have slope = +-1%2Fm+=+-24%2F7+
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given: P( -2,4)
Use the general point-slope formula:
+%28+y+-+4+%29+%2F+%28+x+-%28-2%29+%29+=+-24%2F7+
+y+-+4+=+%28+-24%2F7+%29%2A%28+x+%2B+2+%29+
+y+-+4+=+%28-24%2F7%29%2Ax+-+24%2F5+
+y+=+%28-24%2F7%29%2Ax+-+4%2F5+ answer
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Solve the equations to find their intersection:
+y+=+%287%2F24%29%2Ax+%2B+5%2F12+
+y+=+%28-24%2F7%29%2Ax+-+4%2F5+
------------------------
+24y+=+7x+%2B+10+
+7x+-+24y+=+-10+
and
+7y+=+-24x+-+28%2F5+
+24x+%2B+7y+=+-28%2F5+
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This is very tough- solve for x and y which
gives you the point on the given line
Now you have 2 points P and Q on the perpendicular line
Use the length equation:
+d+=+sqrt%28+%28+x%5B2%5D+-+x%5B1%5D+%29%5E2+%2B+%28+y%5B2%5D+-+y%5B1%5D+%29%5E2+%29+