Question

Emma is using a straightedge and compass to do the construction shown.


Which best describes the construction Emma is doing?

• A. a line through $P$ parallel to line $l$
• B. a line through $P$ intersecting line $l$
• C. a line through $P$ perpendicular to line $l$
• D. None of the above

Answer 1

The correct option is A a line through $P$ parallel to line $l$

$\underset{–}{\text{Steps to draw a line through O parallel to line AB}}$

1. Draw a transverse line through point $O$ across line $AB,$ at any angle
2. Draw an arcfrom the intersectionpoint of line $AB$ and the transversal
3. Using the same radius, draw an arc at point $O$
4. Measure the distance between the points where the arc intersects line $AB$ and the transversal
5. With the same length, draw an arc, centered at the intersection point of the earlier arc and ray
6. Draw a line through $O$ and the intersection point of the two arcs.

Hence, the diagram in question, describes a line through $P$ parallel to line $l$