Your teacher will grade your responses for questions 7–9 to ensure that you receive proper credit for your answers. Given ΔGHI with G(4, –3), H(–4, 2), and I(2, 4), find the perpendicular bisector of in standard form. (2 points)
be sure to give an original response please
To find the perpendicular bisector of segment GH in standard form, we first need to find the midpoint of GH. The midpoint can be calculated using the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Given that G(4, -3) and H(-4, 2), the midpoint (M) can be calculated as follows:
M = ((4 + -4) / 2, (-3 + 2) / 2)
M = (0, -0.5)
Next, we need to determine the slope of GH. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
Slope (m) = (y2 - y1) / (x2 - x1)
Using G(4, -3) and H(-4, 2),
m = (2 - (-3)) / (-4 - 4)
m = 5 / (-8)
m = -5/8
Since the perpendicular bisector of a line has a negative reciprocal slope, the slope of the perpendicular bisector (m') is:
m' = -1 / m
m' = -1 / (-5/8)
m' = 8/5
Now, we have the midpoint (0, -0.5) and the slope 8/5. We can substitute these values into the standard form equation of a line:
Ax + By = C
Substituting (0, -0.5) and 8/5:
8/5(0) + B(-0.5) = C
0 + (-4/5)B = C
C = (-4/5)B
Thus, the equation of the perpendicular bisector in standard form is:
8/5x + (-4/5)y = (-4/5)B
This equation represents the perpendicular bisector of segment GH.