Nitha Mulungu
Jul 13
Find the equation of straight line which is equidistant from the lines y=1 and y=-5?
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ChatGPT
Jul 13
To find the equation of the line that is equidistant from the lines y=1 and y=-5, we first need to find the midpoint between the two lines.
The midpoint between two parallel lines is the average of their y-intercepts. The y-intercepts of the lines y=1 and y=-5 are 1 and -5, respectively. So, the midpoint between these two lines is:
Midpoint = (1 + (-5)) / 2 = -2 / 2 = -1
Therefore, the line that is equidistant from the lines y=1 and y=-5 passes through the point (0, -1).
Now, since the line is equidistant from the two lines, it must be parallel to them. The slope of the line y=1 is 0 and the slope of the line y=-5 is also 0. Therefore, the slope of the line that is equidistant from the two lines is also 0.
So, the equation of the line that is equidistant from the lines y=1 and y=-5 is:
y = -1
Therefore, the equation of the line that is equidistant from the lines y=1 and y=-5 is y = -1.
The midpoint between two parallel lines is the average of their y-intercepts. The y-intercepts of the lines y=1 and y=-5 are 1 and -5, respectively. So, the midpoint between these two lines is:
Midpoint = (1 + (-5)) / 2 = -2 / 2 = -1
Therefore, the line that is equidistant from the lines y=1 and y=-5 passes through the point (0, -1).
Now, since the line is equidistant from the two lines, it must be parallel to them. The slope of the line y=1 is 0 and the slope of the line y=-5 is also 0. Therefore, the slope of the line that is equidistant from the two lines is also 0.
So, the equation of the line that is equidistant from the lines y=1 and y=-5 is:
y = -1
Therefore, the equation of the line that is equidistant from the lines y=1 and y=-5 is y = -1.
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Google Gemini AI
Jul 13
The equation of a straight line equidistant from the lines y = 1 and y = - 5 is the perpendicular bisector of the line segment joining the points (0, 1) and (0, -5).
The midpoint of the line segment joining the points (0, 1) and (0, -5) is ((0+0)/2, (1-5)/2) = (0, -2).
The slope of the line segment joining the points (0, 1) and (0, -5) is (1 - (-5))/(0 - 0) = 6/0, which is undefined.
Hence, the line segment joining the points (0, 1) and (0, -5) is vertical. Therefore, the perpendicular bisector is a horizontal line passing through the midpoint (0, -2).
Therefore, the equation of the straight line is y = -2.
The midpoint of the line segment joining the points (0, 1) and (0, -5) is ((0+0)/2, (1-5)/2) = (0, -2).
The slope of the line segment joining the points (0, 1) and (0, -5) is (1 - (-5))/(0 - 0) = 6/0, which is undefined.
Hence, the line segment joining the points (0, 1) and (0, -5) is vertical. Therefore, the perpendicular bisector is a horizontal line passing through the midpoint (0, -2).
Therefore, the equation of the straight line is y = -2.
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