Question

Line AB passes through points A(-6,7) and B(-6,-3) as shown on the coordinate grid below.

Determine the equation of a line that is perpendicular to line AB and passes through the point (2, 4).

Answer 1

The equation of a line that is perpendicular to line AB and passes through the point (2, 4) is y = 4, as AB is a vertical line and the perpendicular line is horizontal with a slope of 0.

Step-by-step explanation:

The question asks to determine the equation of a line that is perpendicular to line AB and passes through the point (2, 4). Because line AB is vertical, as both points A and B have the same x-coordinate (-6), the slope is undefined, meaning it is perpendicular to a horizontal line. A line that is horizontal and thus perpendicular to AB will have a slope of 0.

To find the equation of the line that is perpendicular to AB and passes through the point (2, 4), we can use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Since the slope (m) is 0 for a horizontal line, the equation simplifies to y = y1.

Therefore, the equation of the line that is perpendicular to AB and passes through the point (2, 4) is simply y = 4.