Question 1208624
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<font color=red>Answer: </font> {{{y = expr(1/2)x + 2}}}


Explanation


Let D be the midpoint of segment BC.
Use the midpoint formula, or follow a process similar to <a href="https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1208318.html">this question</a>, to find that D = (-2,1)


The equation we want to find is through A(4,4) and D(-2,1)
Let's find the slope of this line.
{{{matrix(1,15,"Given","points:","(",x[1],",",y[1],") = ","(4,4)","and","(",x[2],",",y[2],") = ","(-2,1)")}}}


{{{m = slope = rise/run = matrix(1,3,"change","in","y")/matrix(1,3,"change","in","x")}}}


{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (1 - 4)/(-2 - 4)}}}


{{{m = (-3)/(-6)}}}


{{{m = 1/2}}}
The slope of line AD is 1/2



Now apply point-slope form and solve for y.
{{{y-y[1] = m(x - x[1])}}}


{{{y-y[1] = expr(1/2)(x - x[1])}}} Plug in the slope


{{{y-4 = expr(1/2)(x - 4)}}} Plug in the coordinates of point A (you could also use the coordinates of point D)


{{{y-4 = expr(1/2)x - 2}}}


{{{y-4 = expr(1/2)x - 2+4}}}


{{{y = expr(1/2)x + 2}}}
This equation has slope 1/2 and y intercept 2.


{{{
drawing(500,500,-7,5,-3,7,
graph(500,500,-7,5,-3,7,-100,-100,0.5x+2),
circle(4,4,0.05),circle(4,4,0.07),circle(4,4,0.09),circle(4,4,0.11),circle(-6,2,0.05),circle(-6,2,0.07),circle(-6,2,0.09),circle(-6,2,0.11),circle(2,0,0.05),circle(2,0,0.07),circle(2,0,0.09),circle(2,0,0.11),circle(-2,1,0.05),circle(-2,1,0.07),circle(-2,1,0.09),circle(-2,1,0.11),
line(4,4,-6,2),line(-6,2,2,0),line(2,0,4,4),
locate(4.2,3.8,"A"),locate(-5.8,1.8,"B"),locate(2.2,-0.2,"C"),locate(-1.8,0.8,"D")
)
}}}
The equation of the line {{{y = expr(1/2)x + 2}}} is in blue.


You can use a tool like <a href="https://www.geogebra.org/">GeoGebra</a> to verify the answer. <a href="https://www.desmos.com/calculator">Desmos</a> is also a good choice.
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