SOLUTION: Find C such that (10,-1), (-4,10), and (C,-6) lie on a line. What is the C value?

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Question 1203671: Find C such that (10,-1), (-4,10), and (C,-6) lie on a line. What is the C value?
Found 3 solutions by ikleyn, MathLover1, josgarithmetic:
Answer by ikleyn(52781) About Me  (Show Source):
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Find C such that (10,-1), (-4,10), and (C,-6) lie on a line. What is the C value?
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Write an equation saying that the slope of the segment PQ, where P= (10,-1), Q= (-4,10),
is the same as the slope of the segment QR, where R= (C,-6).

The slope of the segment PQ is  %2810-%28-1%29%29%2F%28-4-10%29 = 11%2F%28-14%29 = -11%2F14.

The slope of the segment QR is  %28-6-10%29%2F%28C-%28-4%29%29 = %28-16%29%2F%28C%2B4%29.


So, the equation is

    -16%2F%28C%2B4%29 = -11%2F14.


It implies

    16%2F%28C%2B4%29 = 11%2F14

    16*14 = 11*(C+4)

     224  = 11C + 44

     224 - 44 = 11C

        180   = 11C

         C    = 180%2F11 = 164%2F11.    ANSWER

Solved.



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Find +C+ such that (+10 ,+-1 ), (+-4 ,+10 ), and (+C ,+-6 ) lie on a line. What is the +C value?

the slope of the line can be calculated using the slope formula:

+m=%28y2-y1%29%2F%28x2-x1%29
+m=%2810-%28-1%29%29%2F%28-4-10%29
+m=%2810%2B1%29%2F%28-14%29
+m=-11%2F14

We know that the slope between the two points (+10 ,+-1 ) and (+C ,+-6 ) is also equal to +-11%2F14

that is, we can set up an equation involving +C and solve for +C

+%28-6-%28-1%29%29%2F%28C-10%29=-11%2F14
+%28-6%2B1%29%2F%28C-10%29=-11%2F14
+-5%2F%28C-10%29=-11%2F14
+-5%2A14=-11%28C-10%29
-70=-11C%2B110
+11C=70%2B110
+C=180%2F11

answer is:
+C+=+180%2F11

and the point is:
(+180%2F11 ,+-6 )

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
slope %2810-%28-1%29%29%2F%28-4-10%29, 11%2F%28-14%29, -11%2F14

y=mx%2Bb
y-b=mx
b=y-mx
Take one of the given points and evaluate b.

b=-1-%28-11%2F14%2910=-1%2B110%2F14=-1%2B55%2F7=-7%2F7%2B55%2F7=47%2F7

equation for the line, y=-%2811%2F14%29x%2B47%2F7.

Want C when y=-6.
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