Question

When constructing a line parallel to a given line, i, through a point, p, not on the given line, you will be:

a. Applying the Pythagorean Theorem.
b. Using the midpoint formula.
c. Employing the slope-intercept form of a line.
d. Utilizing the parallel line postulate.

Answer 1

To construct a line parallel to a given line through a point not on the line, utilize the parallel line postulate and the slope-intercept form of a line.

Step-by-step explanation:

When constructing a line parallel to a given line, i, through a point, p, not on the given line, you will be utilizing the parallel line postulate. According to the postulate, if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel. In this case, the given line and the parallel line will have the same slope, which can be found using the slope-intercept form of a line, y = mx + b.

Step 1: Determine the slope of the given line, i, using the slope-intercept form.

Step 2: Use the slope found in step 1 and the coordinates of point p to write the equation of the parallel line using the slope-intercept form.

Step 3: Graph the given line, i, and the parallel line to visually verify that they are parallel.