Which equation represents the perpendicular bisector of AB whose endpoints are A(8,2) and B(0,6)?
10 y=2x-4
20 y=-1/2x=2
3) y=-1/2x =6
4)y=2x-12
So I did Delta Y over Delta X and got -4/8 or -.5. Since it says perpendicular I made it the opposite sign and flipped it and got 8/4 or 2. Then I plugged it into y=mx+b. I plugged it in using B and did 6=2(o)=b and got 6 for b but 2x-6 isn't an answer choice. SO then I used A and got 2=2(8)=b and got b = -14 which is also not an answer choice.
What am i doing wrong?
Which line goes through midpoint (4,4) and has slope -1/[4/-8] = 2 ?
Only choices 1 and 4 have the correct slope.
Only #1 goes through 4,4.
To find the equation of the perpendicular bisector of AB, we need to follow these steps:
1. Find the midpoint of AB:
The midpoint (M) of AB is the average of the x-coordinates and the average of the y-coordinates of A and B.
Midpoint (M) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
In this case, the coordinates of A are (8, 2) and the coordinates of B are (0, 6)
So, the midpoint (M) = ((8 + 0)/2, (2 + 6)/2) = (4, 4)
2. Calculate the slope of AB:
The slope (m) of AB can be found using the slope formula:
m = (y₂ - y₁)/(x₂ - x₁)
In this case, the coordinates of A are (8, 2) and the coordinates of B are (0, 6)
So, the slope (m) = (6 - 2)/(0 - 8) = 4/(-8) = -1/2
3. Find the negative reciprocal of the slope of AB:
To find the slope of the perpendicular bisector, we take the negative reciprocal of the slope of AB.
So, the slope of the perpendicular bisector = -1/m = -1/(-1/2) = 2
4. Use the midpoint and slope to find the equation:
We have the slope (m = 2) and the midpoint (M = (4, 4)), so we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
Plugging in the values, we get:
y - 4 = 2(x - 4)
y - 4 = 2x - 8
y = 2x - 8 + 4
y = 2x - 4
So, the equation representing the perpendicular bisector of AB is y = 2x - 4.
Therefore, none of the given answer choices (10 y = 2x - 4, 20 y = -1/2x + 2, 3) y = -1/2x + 6, 4) y = 2x - 12) are correct. The correct answer is y = 2x - 4.
To determine the equation of the perpendicular bisector, you need to find the slope and midpoint of line segment AB. Let's follow the steps:
1. Find the midpoint.
The midpoint of a line segment with endpoints A(x1, y1) and B(x2, y2) can be found using the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, the coordinates of A are (8, 2), and the coordinates of B are (0, 6).
Applying the formula, we get:
Midpoint = ((8 + 0) / 2, (2 + 6) / 2)
= (4, 4)
So, the midpoint of line segment AB is (4, 4).
2. Find the slope.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the slope formula:
Slope = (y2 - y1) / (x2 - x1)
Using the coordinates of A and B, we have:
Slope = (6 - 2) / (0 - 8)
= 4 / -8
= -1/2
So, the slope of line segment AB is -1/2.
3. Find the negative reciprocal of the slope.
Since the perpendicular bisector of AB should have a slope that is the negative reciprocal of -1/2, the negative reciprocal is 2/1 or simply 2.
4. Plug in the midpoint and slope into the point-slope form.
The point-slope form of a linear equation is: y - y1 = m(x - x1)
Using the midpoint (4, 4) and the slope 2, we have:
y - 4 = 2(x - 4)
Simplifying this equation further:
y - 4 = 2x - 8
y = 2x - 8 + 4
y = 2x - 4
Therefore, the correct equation representing the perpendicular bisector of AB is y = 2x - 4, which is option 1 in your list.