Math 444 10/13: Class Exercise on Constructing Lengths from Ratios

A.  Solving x/a = ratio

Given the 3 segments a, b, c above.  Construct these segments on a different sheet.

(1)   Construct a segment of length x, so that x/a = b/c.

(2)   Construct a segment of length y, so that y/a = c/b.

B. Dividing a segment internally and externally

On a separate sheet, draw a segment m = AB congruent to AB below. Construct a point C on line AB that divides AB internally in the ratio AC/CB = c/b.

Given the same segment AB, construct a point D on line AB that divides AB externally in the ratio AD/BD = c/b.

C. Scaling a segment by a given ratio.

Given the segment EF below, construct a point G so that EG/EF = 2/7.

Segment for Problem B