Question

Consider the partial construction of a line parallel to liner through point Q.

What would be the final step in the construction?
Draw a line through P and S.
Draw a line through W and S.
Draw a line through Q and S.
Draw a line through T and S.

Answer 1

The final step in constructing a line parallel to another line through a given point typically involves drawing a line through the given point and the intersection point created by arcs from the given point and the original line.

To construct a line parallel to another through a given point not on the line, one would typically use a ruler and compass in classic geometric construction.

This process involves drawing a line from the given point to intersect the existing line at a right angle, creating a perpendicular transversal.

Then, with the use of a compass set to the width of the intersection to the original point on the line, arcs would be drawn from the given point and from the original intersection that would intersect each other.

The line connecting the intersection of these arcs with the given point completes the parallel line construction.

The final step mentioned in this question is not fully clear without a visual reference or more context, however, in general, drawing a line through the point labeled 'S' (presumably the point of intersection of the arcs) and the given point 'Q' would often be the method to complete the parallel line construction.

Answer 2

Option (3)

Explanation:

To construct a line parallel to the line through point Q we will follow the following steps,

1). We join two points P (on the line) and point Q above the line PT with the help of a straightedge.

2). Now we will copy the angle QPT at point P with the help of a compass (Arcs as shown in the figure)

3). Finally we will join points Q and S to construct a line QS parallel to the line PT.

Therefore, Option (3) will be the answer.