Question

80 POINTS!!!

Answer 1

Answer:

1). Slope = (-2)

2). Midpoint = (2, -2)

3). Slope of the perpendicular bisector = (1/2)

4). Equation of perpendicular bisector will be x - 2y = 6

Step-by-step explanation:

A line segment has the endpoints at (4, -6) and (0, 2).

1). Then the slope of the given line segment will be = (y - y')/(x - x') = (2 + 6)/(0 - 4) = 8/(-4) = (-2)

2). Mid point of the line segment is given by $(\frac{x_{1}+x_{2}}{2}) , (\frac{y_{1}+y_{2}}{2})$

Therefore midpoints of the line segment will be $\frac{4+0}{2},\frac{-6+2}{2}$ = (2, -2)

3). Slope of the perpendicular bisector is represented by $m_{1}.m_{2}=(-1)$

⇒ (-2)×m2 = (-1)

⇒ $m_{2}=\frac{1}{2}$

4). Now we have to find the equation of perpendicular bisector passing through (2, -2) and slope (1/2).

Since standard equation of the line will be given as y = mx + c

$y=\frac{1}{2}x+c$ passes through (2, -2).

$(-2) = \frac{1}{2}(2) + c$

c = (-1) - 2 = -3

Finally the equation of perpendicular bisector will be

$y=\frac{1}{2}x+(-3)$

⇒ 2y = x - 6

⇒ 2y - x = -6

⇒ x - 2y = 6

Answer 2

Answer:

Y=(1/2)x-3

Since the other person got the last one wrong imma put it here

Step-by-step explanation: