A is the point (5,5). B is the point (3,1). Find the equation of the line perpendicular to AB and passing throught the midpoint of AB. I worked out the midpoint to be (4,3) but I don't understand how to do the rest as we haven't done this in class yet.
Could you please tell me how to do it. If you do I will give you best answer if it is right and you explain it. Thank you :)
Could you please tell me how to do it. If you do I will give you best answer if it is right and you explain it. Thank you :)
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Step 1: Find the slope of AB:
slope = (y2-y1)/(x2-x1) = (5-1)/(5-3) = 4/2 = 2
slope of line perpendicular line = -0.5
That is because the product of the slope of a line and a line perpendicular to it should be -1
Now use the point-slope equation:
y-y1 = m(x-x1)
y - 3 = -0.5(x - 4)
Simplify:
y - 3 = -0.5x + 2
y = -0.5x + 5 ----> y = -x/2 +5
Both are correct
slope = (y2-y1)/(x2-x1) = (5-1)/(5-3) = 4/2 = 2
slope of line perpendicular line = -0.5
That is because the product of the slope of a line and a line perpendicular to it should be -1
Now use the point-slope equation:
y-y1 = m(x-x1)
y - 3 = -0.5(x - 4)
Simplify:
y - 3 = -0.5x + 2
y = -0.5x + 5 ----> y = -x/2 +5
Both are correct
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The point-slope form of the equation of a line
y - y1 = m(x - x1)
where (x1, y1) is the known point and m is the slope of the line.
You have correctly computed the midpoint (4, 3). This makes the above equation become:
y - 3 = m(x - 4)
The slope of a line perpendicular to a line of slope (m) is the negative reciprocal of the slope.
Use the two points (5, 5) and (3,1) to compute (m) using the following equation:
m = (y1 - y2)/(x1 - x2) = (5 -1)/(5 - 3) = 4/2 = 2
This makes the slope of the line perpendicular to the line segment = -1/2
The equation becomes:
y - 3 = (-1/2)(x - 4)
You may use algebra to put it into any form you like.
y - y1 = m(x - x1)
where (x1, y1) is the known point and m is the slope of the line.
You have correctly computed the midpoint (4, 3). This makes the above equation become:
y - 3 = m(x - 4)
The slope of a line perpendicular to a line of slope (m) is the negative reciprocal of the slope.
Use the two points (5, 5) and (3,1) to compute (m) using the following equation:
m = (y1 - y2)/(x1 - x2) = (5 -1)/(5 - 3) = 4/2 = 2
This makes the slope of the line perpendicular to the line segment = -1/2
The equation becomes:
y - 3 = (-1/2)(x - 4)
You may use algebra to put it into any form you like.
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The slope of AB = (y1 - y2)/(x1 - x2) where A = (x1, y1) and B = (x2, y2) or A = (x2, y2) and B =(x1, y1).
slope of AB = (5 - 1)/(5 - 3) = 4/2 = 2
Notice that likewise, slope of AB = (1 - 5)/(3 - 5) = -4/(-2) = 2
Perpendicular lines have slopes that are negative reciprocals of each other.
Therefore, the slope of the perpendicular line is -1/2.
Substitute the midpoint (4, 3) for (x1, y1) and -1/2 for m in
y - y1 = m(x - x1) to find the equation of the perpendicular line.
y - 3 = -1/2(x - 4)
y - 3 = -x/2 + 4
y = -x/2 + 7
slope of AB = (5 - 1)/(5 - 3) = 4/2 = 2
Notice that likewise, slope of AB = (1 - 5)/(3 - 5) = -4/(-2) = 2
Perpendicular lines have slopes that are negative reciprocals of each other.
Therefore, the slope of the perpendicular line is -1/2.
Substitute the midpoint (4, 3) for (x1, y1) and -1/2 for m in
y - y1 = m(x - x1) to find the equation of the perpendicular line.
y - 3 = -1/2(x - 4)
y - 3 = -x/2 + 4
y = -x/2 + 7
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The midpoint of the two points is
( (5+3)/2 , (5+1)/2 ) = (4,3)
The slope of the line connecting the points is
(5-1)/(5-3) = 2
Hence the perpendicular line has the negative reciprocal of that slope, and the equation of the line can be written directly in point slope form:
( y - 3 ) = (-0.5)( x - 4 )
or: y = -x/2 + 5
( (5+3)/2 , (5+1)/2 ) = (4,3)
The slope of the line connecting the points is
(5-1)/(5-3) = 2
Hence the perpendicular line has the negative reciprocal of that slope, and the equation of the line can be written directly in point slope form:
( y - 3 ) = (-0.5)( x - 4 )
or: y = -x/2 + 5