SOLUTION: Precalculus Michael Sullivan Section 1.1 Q. 69 When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and subsequent

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Question 1210652: Precalculus
Michael Sullivan
Section 1.1
Q. 69
When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and subsequently will form an ERROR TRIANGLE. If this error triangle is long and thin, one estimate for the location of the desired point is the midpoint of the shortest side.
Let A, B, and C = three lines in quadrant I on the xy-plane. Plot all three lines in quadrant I on the xy-plane. Connect the three lines through the given three points.
A meets B at the point (2.7, 1.7).
A meets C at the point (2.6, 1.5).
B meets C at the point (1.4, 1.3).
(I) Find an estimate for the desired intersection point.
(II) Find the length of the median for the midpoint found in part I.
Found 2 solutions by KMST, ikleyn:
Answer by KMST(5404) About Me  (Show Source):
You can put this solution on YOUR website!


(I) Find an estimate for the desired intersection point.
In this case this error triangle is long and thin, so "one estimate for the location of the desired point is the midpoint of the shortest side".
That midpoint is halfway between points (2.6,1.5) and (2.7,1.7).The coordinates of that midpoint are x=%282.6%2B2.7%29%2F2=2.65 and y=%281.5%2B1.7%29%2F2=1.6
The answer is point highlight%28%22%282.65%2C1.6%29%22%29

(II) Find the length of the median for the midpoint found in part I.
The median in a triangle is the line that connect the midpoint of one side to the opposite vertex.
We already have the midpoint of the short side, and the opposite vertex is obviously %22%281.4%2C1.3%29%22
The length of the median we look for is the distance between %22%281.4%2C1.3%29%22 and %22%282.65%2C1.6%29%22 :
%22=%22highlight%28sqrt%281.6525%29%29%22=%22%22approximately%22%291.2555

Answer by ikleyn(53956) About Me  (Show Source):
You can put this solution on YOUR website!
.
When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and
subsequently will form an ERROR TRIANGLE. If this error triangle is long and thin, one estimate for the location
of the desired point is the midpoint of the shortest side.
Let A, B, and C = three lines in quadrant I on the xy-plane. Plot all three lines in quadrant I on the xy-plane.
Connect the three lines through the given three points.
A meets B at the point (2.7, 1.7).
A meets C at the point (2.6, 1.5).
B meets C at the point (1.4, 1.3).
(I) Find an estimate for the desired intersection point.
(II) Find the length of the median for the midpoint found in part I.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


In the post by @KMST,  all calculations are correct except of the last one.

Her answer to question (II)   " highlight%28sqrt%281.6525%29%29%22=%22%22approximately%22%291.2555 "   is incorrect.

The correct answer is   highlight%28sqrt%281.6525%29%29%22=%22%22approximately%22%291.2855.

Find the difference.