Answer: y+5 = (11/3)(x-7) which can be written as [tex]y+5 = \frac{11}{3}(x-7)[/tex]
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Explanation:
A = (-4,-2) C = (18,-8) D = midpoint of segment AC D = (p,q) p = ((x coordinate of A)+(x coordinate of C))/2 p = ((-4)+(18))/2 p = 14/2 p = 7 q = ((y coordinate of A)+(y coordinate of C))/2 q = ((-2)+(-8))/2 q = -10/2 q = -5 The midpoint of segment AC is D = (p,q) = (7,-5)
Now let's find the slope of line AC m = (y2-y1)/(x2-x1) m = (-8-(-2))/(18-(-4)) m = (-8+2)/(18+4) m = -6/22 m = -3/11
Flip the fraction and the sign of the slope flip the fraction: -3/11 ----> -11/3 and flip the sign from positive to negative: -11/3 ----> +11/3 = 11/3
The answer will have a slope of 11/3 and the line goes through D = (7,-5), so using point slope form we can say: y-y1 = m(x-x1) y-(-5) = (11/3)(x-7) y+5 = (11/3)(x-7)
which why the answer is y+5 = (11/3)(x-7) and it can be written as [tex]y+5 = \frac{11}{3}(x-7)[/tex] In the first version mentioned above, the 11/3 is in its own set of parenthesis to indicate to multiply all of 11/3 by the quantity (x-7). We aren't simply multiplying the 3 only.
