Triangle ABC has the following points: A (-2,-2), B (4,4), C (18,-6). Use these points to write the equations of the line containing the perpendicular bisector of AC
To find the equation of the line containing the perpendicular bisector of AC, we first need to find the midpoint of AC.
The midpoint of AC can be found using the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the coordinates of A are (-2, -2) and the coordinates of C are (18, -6).
Midpoint = ((-2 + 18)/2, (-2 + -6)/2)
Midpoint = (8, -4)
Now that we have the midpoint, we can find the slope of the line containing AC using the slope formula:
Slope = (y2 - y1)/(x2 - x1)
In this case, the coordinates of A are (-2, -2) and the coordinates of C are (18, -6).
Slope = (-6 - (-2))/(18 - (-2))
Slope = (-6 + 2)/(18 + 2)
Slope = -4/20
Slope = -1/5
The slope of a line perpendicular to AC will be the negative reciprocal of the slope of AC. So, the slope of the perpendicular bisector of AC will be 5.
Now that we have the midpoint (8, -4) and the slope of the perpendicular bisector of AC (5), we can write the equation of the line using the point-slope form:
y - y1 = m(x - x1)
Using the values found:
y - (-4) = 5(x - 8)
Simplifying the equation:
y + 4 = 5x - 40
y = 5x - 44
Therefore, the equation of the line containing the perpendicular bisector of AC is y = 5x - 44.