Answer:
The equation of the line segment to the line segment with end point (4, 4) and (-8, 8) is y = x/3 - 4
Step-by-step explanation:
The coordinates of the given points are;
(4, 4) and (-8, 8)
Therefore;
![Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=Slope%2C%20%5C%2C%20m%20%3D%5Cdfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
Where;
y₁ = 4, y₂ = -8, x₁ = 4, x₂ = 8
Therefore, the slope, m of the given line segment = (-8 - 4)/(8 - 4) = -3
The slope of the perpendicular line segment = -1/m = -1/(-3) = 1/3
The mid point of the line segment with endpoint (4, 4) and (-8, 8) is given as follows;
![Midpoint, M = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )](https://tex.z-dn.net/?f=Midpoint%2C%20M%20%3D%20%5Cleft%20%28%5Cdfrac%7Bx_1%20%2B%20x_2%7D%7B2%7D%20%2C%20%5C%20%5Cdfrac%7By_1%20%2B%20y_2%7D%7B2%7D%20%5Cright%20%29)
Therefore, the midpoint = ((4 + 8)/2, (4 + (-8))/2) = (6, -2)
The equation of the perpendicular line segment in point and slope form is given as follows;
y - (-2) = 1/3 × (x - 6)
Which gives;
y + 2 = x/3 - 6/3 = x/3 - 2
y = x/3 - 2 - 2 = x/3 - 4
The equation of the line segment to the line segment with end point (4, 4) and (-8, 8) is y = x/3 - 4