SOLUTION: find the point (x,y) on the line y+-4x-5 that is equidistant from the points (8,-10) and (-7,0)

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Question 556013: find the point (x,y) on the line y+-4x-5 that is equidistant from the points (8,-10) and (-7,0)
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Still no equal sign

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +y+=+4x+-+5+
(2)
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This is 2 equations and 2 unknowns, so it's solvable
(1) +4x+-+y+=+5+
and
(2) +%28+x+-+8+%29%5E2+%2B+%28+y+%2B+10+%29%5E2+=+%28+x+%2B+7+%29%5E2+%2B++y%5E2+
(2) +x%5E2+-+16x+%2B+64+%2B+y%5E2+%2B+20y+%2B+100+=+x%5E2+%2B+14x+%2B+49+%2B+y%5E2+
(2) +-16x+%2B+20y+%2B+64+%2B+100+=+14x+%2B+49+
(2) +14x+%2B+16x+-+20y+=+164+-+49+
(2) +30x+-+20y+=+115+
(2) +6x+-+4y+=+23+
Multiply both sides of (1) by 4
and subtract (1) from (2)
(2) +6x+-+4y+=+23+
(1) +-16x+%2B+4y+=+-20+
+-10x+=+3+
+x+=+-%283%2F10%29+
and, since
(1) +y+=+4x+-+5+
(1) +y+=+-%2812%2F10%29+-+5+
(1) +y+=+-%286%2F5%29+-%2825%2F5%29+
(1) +y+=+-%2831%2F5%29+
(x,y) = (-3/10, -31/5 )
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check:
(1) +y+=+4x+-+5+
(1) +-%2831%2F5%29+=+4%2A%28-3%2F10%29+-+5+
(1) +-%2831%2F5%29+=+-%2812%2F10%29+-+25%2F5+
(1) +-%2831%2F5%29+=+-%286%2F5%29+-%2825%2F5%29+
(1) +-%2831%2F5%29+=+-%2831%2F5%29+
OK
(2)
(2)
(2) +%28-83%2F10%29%5E2+%2B+%2819%2F5%29%5E2+=+%2867%2F10%29%5E2+%2B+%28-31%2F5%29%5E2+
(2) +%28-83%2F10%29%5E2+%2B+%2838%2F10%29%5E2+=+%2867%2F10%29%5E2+%2B+%28-62%2F10%29%5E2+
(2) +68.89+%2B+14.44+=+44.89+%2B+38.44+
(2) +83.33+=+83.33+
OK