In the trapezoid abcd (
ab
∥
cd
) point m∈
ad
, so that am: md=3: 5. line l ∥
ab
and going trough point m intersects diagonal
ac
and leg
bc
at points p and n respectively. find:

ap: pc and bn: cn

  AP:PC = BN:CN = 3:5

Step-by-step explanation:

The horizontal line MN divides any line between AB and CD into the same ratio as AM:MD, which is 3:5.

  AP:PC = BN:CN = 3:5

_____

Since MP is parallel to AC, triangles AMP and ADC are similar with the scale factor AM:AD = 3:8. Likewise, triangles CNP and CBA are similar with the scale factor 5:8. These similarities and scale factors make ...

  (AP+PC)/AP = 8/3

  1 +PC/AP = 1 +5/3 . . . . . rewrite

  AP/PC = 3/5 . . . . . . . . .subtract 1 and invert

__

  (CN+BN)/CN = 8/5

  1 +BN/CN = 1 +3/5 . . . . . rewrite

  BN/CN = 3/5 . . . . . . . . . subtract 1

this answer is !

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: