Question

Can someone help me with these? I’m having confusion with these problems. If you can help, can you possibly show me on a paper on how to do this?

Answer 1

Answer:

  see attachment

Step-by-step explanation:

To work these, you need a pencil (with a fairly sharp point) and a compass or pair of dividers (a compass-like tool with two points, instead of a point and a pencil).

In the attached, the blue segment represents the compass set to the length of segment 'a'. The red segment represents the compass set to the length of segment 'b', and the green segment represents the compass set to the length of segment 'c'.

When the segments are shown end-to-end, it means you mark off that length on the line, then mark off the next length starting at the end of the first one. When the segments are shown overlapping, it means you mark one of the segments in the reverse direction (you subtract its length).

You may find it helpful to use your pencil to mark a starting point on the target line. If you use a compass, a small arc across the target line at the end of the segment length can help you locate the start of the next segment length.

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(1) The length of segment 'b' is added to the length of segment 'a'. This is not different in concept from adding numbers on a number line.

(2) The length of segment 'b' is made to overlap the end of segment 'a', so that the end points of the two segments are the same point. This subtracts the length of 'b' from that of 'a', so the length 'a-b' is the length from the left end of 'a' to the left end of 'b' in the configuration shown.

(3) You get the length '2b' by appending the length of 'b' to itself.

(4) All three lengths are appended to each other here.

(5) As before, you get 2b by appending 'b' to itself. You subtract 'c' by backtracking over the previous length, as in part (2).

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You will get best results if you use this (attachment) as a guide. The line segments drawn are only eyeball approximations of the segments on your page, and their placement end-to-end is not as precise as you can make it with your compass.