A line segment is bisected by a line with the equation #  y + 7 x = 1 #. If one end of the line segment is at #( 7 , 2 )#, where is the other end?
Find the equation of a line that is perpendicular to the give line and goes through (7,2), then use the midpoint formula.
Since a segment's perpendicular bisector passes through its midpoint, the intersection of the two lines represents the segment's midpoint. Next, apply the midpoint formula to determine the segment's other endpoint.
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To find the other end of the line segment, we can first determine the coordinates of the point where the bisecting line intersects the line segment. Then, using these coordinates, we can calculate the coordinates of the other end of the line segment.

Find the slope of the bisecting line by rearranging its equation into slopeintercept form (y = mx + b). y + 7x = 1 y = 7x + 1 y = 7x  1

The slope of the bisecting line is 7.

The negative reciprocal of the slope of the bisecting line gives the slope of the line segment, which is 1/7.

Use the pointslope form of the equation of a line (y  y1 = m(x  x1)), with the known point (7, 2) and the calculated slope (1/7) to find the equation of the line containing the line segment. y  2 = (1/7)(x  7)

Simplify the equation: y  2 = (1/7)x + 1 y = (1/7)x + 3

To find where this line intersects the bisecting line, substitute the equation of the bisecting line (y + 7x = 1) into the equation of the line segment (y = (1/7)x + 3). ((1/7)x + 3) + 7x = 1

Solve for x: (1/7)x  3 + 7x = 1 (1/7 + 7)x = 4 (1/7 + 49/7)x = 4 (50/7)x = 4 x = (4 * 7) / 50 x = 0.56

Substitute x back into the equation of the line segment to find y: y = (1/7)(0.56) + 3 y = 3.2
The other end of the line segment is located at approximately (0.56, 3.2).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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