Question

Which diagram suggests a correct construction of a line parallel

to given line 1 and passing through given point Q?

Answer 1

The correct answer is:

The fourth diagram.

Step-by-step explanation:

To construct a parallel line to line 1 through point Q, we can use perpendicular lines.

We first place our compass on point Q. We draw an arc that intersects line 1 at two points.

We next change the width of our compass and set it on one of the points of intersection of the arc and line 1. We want to draw a small arc below our first one. We then move the compass to the other point of intersection and draw another small arc, intersecting the previous one. Connect this point of intersection of the arcs with point Q; this forms a perpendicular line to line 1.

Move the compass to point Q and construct an arc that intersects this perpendicular line in two points. Set the compass a bit wider and place it at one of the points of intersection for this new arc and our perpendicular line. Construct a small arc outside the previous one. Keeping the compass at the same width, move the compass to the other point of intersection with our perpendicular line and draw another small arc that intersects the previous one. Connect this point with point Q, forming another perpendicular line that is parallel to line 1.

Answer 2

A diagram that suggests a correct construction of a line parallel to given line l and passing through given point Q is: D. diagram D.

In Mathematics and Euclidean Geometry, parallel lines refers to two lines that are always the same distance apart and never meet.

This ultimately implies that, parallel lines are always coplanar lines and straight lines that have an equal distance between each other.

In order to construct a line that is parallel to given line l and passing through point Q, we would apply the concept of perpendicular lines, especially by placing our compass at point Q and then draw an arc that intersects line l at two different points.