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floor plans for a building have four corners of a room located at the points (2,3),(11,6), (-3,18) and (8,21) determine whether the side through the points (2,3) and (11,6) is parallel to the side through the points (-3,18) and (8,21); then determine whether the side through the points (2,3) and (11,6) is perpendicular to the side through the points (2,3) and (-3, 18); I am so confused now I don't know where to begin. this is what I did hope to find if I am on the right track;
m=6-3/11-2 =3/9=1/3 and m= 18-3/-3-2=15/5=3 now I need to find out if it is perpendicular ?
Last edited by jxharmon (2007-01-22 04:46:09)
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Lines which are parallel have the same slope. If you have two points (x1, y1) and (x2, y2), the slope is calculated as (y2 - y1) / (x2 - x1). So the slope of the line going through (2,3) and (11, 6) is (6-3) / (11-2) = 1/3. The slope of the line going through (-3,18) and (8,21) is (21-18) / (8 -(-3)) = 3/11. The slopes aren't the same, so they are not parallel.
If 2 lines are perpendicular, the slope of one will be the negative inverse of the other. For example if the slope of one line is 1/5, the slope of the line perpendicular will be the the inverse of 1/5 (which is 5) multiplied by -1. The slope would be therefore be -5.
We already know the slope of the line going through (2,3) and (11,6) is 1/3. The slope of the line between (2,3) and (-3,18) is (18-3) / (-3-2) = -3. So the slopes are 1/3 and -3. They are negative inverses of each other, so they are perpendicular to each other.
This info can be used for your other post in figuring out if a shape is a square or a parallelogram. A square has perpedicular lines whereas a parellalgram does not (unless it's also a square since all squares are parallelograms).
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thanks that help me get out of the rut
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