Question

which of the following is being constructed in the image.


1. a line parallel to a given line through a point not on the line

2. a perpendicular bisector of a line segment

3. a line perpendicular to a given line through a point not on the line

4. a line segment that is congruent to a given line segment

Answer 1

Answer:

  3. a line perpendicular to a given line through a point not on the line

Step-by-step explanation:

The point not on the line suggests that choices 1 and 3 are possibilities. The fact that the dotted line is not parallel (and is perpendicular) to the solid line suggests that choice 3 is applicable and choice 1 is not.

The short arcs are equidistant from the end points of the chord that intercepts the larger arc. Hence the line through the crossing point of the short arcs and the point on the other side of the line will be the perpendicular bisector of the chord, and will be perpendicular to the solid line. Creating that perpendicular is likely the purpose of the construction.

Answer 2

This is about construction of lines.

The correct answer is option 3; A line perpendicular to a given line through a point not on the line.

• In the Image, we see that the vertical line has already been established and it is the horizontal line that is being constructed.

• Now, from what we see is that there was initially a point towards the left where the horizontal line started from.

• However, with that point alone they couldn't have been able to draw that line to be perpendicular to the vertical one without the next steps.

• What was done was to first pick a point on the vertical line and draw an arc to cut top and bottom of the vertical line.

Then one leg of compass is placed at each point with a fixed distance and another small arc is drawn which we can see to the right intersecting each other.

• This serves as the point that makes a line drawn from the left point through the vertical line to be perpendicularperpendicular.

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