The equation of XZ is:
[tex]y = -x+3[/tex]
Step-by-step explanation:
Given
a(-2,2), b(2,4), c(4,-4)
As the required line passes thought the mid-points of AB and BC so we have to find the mid-points of AB and BC first
So,
[tex]Mid-point\ of\ AB = (\frac{x_a_x_b}{2} , \frac{y_a+y_b}{2})\\(x_1,x_2) = (\frac{-2+2}{2},\frac{2+4}{2})\\(x_1,y_2) =(\frac{0}{2} , \frac{6}{2})\\(x_1,y_2) = (0,3)\\[/tex]
[tex]Mid-point\ of\ BC = (\frac{x_b+x_c}{2}, \frac{y_b+y_c}{2})\\(x_2,y_2) = (\frac{2+4}{2},\frac{4-4}{0})\\= (\frac{6}{2}, \frac{0}{2})\\= (3,0)[/tex]
So,
The two given points are:
X(0,3) and Z(3,0)
First of all, we have to find the slope of the line passing through the given points
So,
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\m = \frac{0-3}{3-0}\\m = \frac{-3}{3}\\m = -1[/tex]
The equation of line is given by:
[tex]y = mx+b[/tex]
Putting the value of slope
[tex]y = -x+b[/tex]
To find the value of b, putting (3,0) in the equation
[tex]0 = -(3)+b\\0 = -3+b\\b = 3[/tex]
So the equation of XZ is:
[tex]y = -x+3[/tex]
Keywords: Equation of line, slope
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