SOLUTION: Plot the points (0,-10), (8,1) and (15,10). How far is the second point from the line joining the other two?

Algebra ->  Points-lines-and-rays -> SOLUTION: Plot the points (0,-10), (8,1) and (15,10). How far is the second point from the line joining the other two?      Log On


   

Question 1123062: Plot the points (0,-10), (8,1) and (15,10). How far is the second point from the line joining the other two?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find slope of line connecting ( 0, -10 ) and ( 15, 10 )
+m%5B1%5D+=+%28+10+-%28-10%29+%29+%2F+%28+15+-+0+%29+
+m%5B1%5D+=+20%2F15+
+m%5B1%5D+=+4%2F3+
———————————
+y+=+%284%2F3%29%2Ax+%2B+b+
+10+=+%284%2F3%29%2A15+%2B+b+
+30+=+60+%2B+3b+
+3b+=+-30+
+b+=+-10+
+y+=+%284%2F3%29%2Ax+-+10+
————————————
Any line perpendicular to this line
Has slope +m%5B2%5D+=+-1%2F%284%2F3%29+
+m%5B2%5D+=+-3%2F4+
——————————-
.+1+=+%28-3%2F4%29%2A8+%2B+b+
+1+=+-6+%2B+b+
+b+=+7+
+y+=+%28-3%2F4%29%2Ax+%2B+7+
——————————
Find intersection of the 2 lines
Subtract the equations
+%284%2F3%29%2Ax+-+10+-%28-3%2F4%29%2Ax+-+7+=+0+
Multiply by 12
+16x+-+120+%2B+9x+-+84+=+0+
+25x+=+204+
+x+=+204%2F25+
—————————-
No time to finish
Check math carefully
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